#5,272

Most Influential Person

American mathematician

Mathematics

#350

World Rank

#724

Historical Rank

#168

USA Rank

Measure Theory

#514

World Rank

#734

Historical Rank

#215

USA Rank

Berndt is the Michio Suzuki Distinguished Research Professor of Mathematics at the University of Illinois. Berndt received his undergraduate degree from Albion College in Michigan in 1961. He received his master’s and Ph.D. in Mathematics from the University of Wisconsin-Madison. With the exception of a year as visiting professor at the University of Glasgow in Scotland and a one-year stint at the Institute for Advanced Study at Princeton, Berndt has enjoyed his long and stellar career teaching and researching mathematics at the University of Illinois.

Berndt is world-famous as one of the greatest analytic number theorists, a core area in mathematics exploring the properties of number systems, such as the integers. He is perhaps best known for working out the results of the singular genius Srinivasa Ramanujan, a “prophet” of mathematics discovered by talents in the United States after solving some of the world’s most difficult problems in mathematics without the benefit of formal and extensive mathematical training. Berndt received a coveted Steele Prize for his work on Ramanujan’s notebooks, and also serves as editor of the Ramanujan Journal.

Berndt was named Fellow of the American Mathematical Society in 2012. In 2012, SASTRA University in India also awarded him an honorary doctorate.

**Featured in Top Influential Mathematicians Today**

According to Wikipedia, Bruce Carl Berndt is an American mathematician. Berndt attended college at Albion College, graduating in 1961, where he also ran track. He received his master's and doctoral degrees from the University of Wisconsin–Madison. He lectured for a year at the University of Glasgow and then, in 1967, was appointed an assistant professor at the University of Illinois at Urbana-Champaign, where he has remained since. In 1973–74 he was a visiting scholar at the Institute for Advanced Study in Princeton. He is currently Michio Suzuki Distinguished Research Professor of Mathematics at the University of Illinois.

- Ramanujan’s Notebooks: Part V (1997) (1829)
- Ramanujan's Notebooks (1985) (1378)
- Ramanujan's Lost Notebook: Part I (2005) (639)
- Number theory in the spirit of Ramanujan (2006) (467)
- Gauss and Jacobi sums (2021) (430)
- Ramanujan’s Theories of Elliptic Functions to Alternative Bases (1995) (246)
- The determination of Gauss sums (1981) (170)
- Ramanujan: Letters and Commentary (1995) (168)
- -Series with Applications to Combinatorics, Number Theory, and Physics (2001) (152)
- Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, p, and the Ladies Diary (1988) (142)
- Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan. (1978) (141)
- Modular transformations and generalizations of several formulae of Ramanujan (1977) (118)
- Ramanujan's Series for 1/π: A Survey (2009) (108)
- Chapter 16 of Ramanujan's Second Notebook Theta Functions and Q-Series (1985) (108)
- Ramanujan’s Unpublished Manuscript on the Partition and Tau Functions with Proofs and Commentary (2001) (94)
- The Number of Zeros for ζ(k)(s) (1970) (84)
- Explicit evaluations and reciprocity theorems for finite trigonometric sums (2002) (81)
- Illinois Journal of Mathematics (1957) (79)
- Ramanujan's lost notebook (2012) (75)
- Ramanujan's lost notebook: Combinatorial proofs of identities associated with Heine's transformation or partial theta functions (2010) (75)
- Sums of gauss, jacobi, and jacobsthal☆ (1979) (74)
- Identities involving the coefficients of a class of Dirichlet series. I (1969) (69)
- Character analogues of the poisson and Euler-MacLaurin summation formulas with applications (1975) (67)
- The Continued fractions found in the unorganized portions of Ramanujan's notebooks (1992) (67)
- Partial Theta Functions (2009) (67)
- Classical theorems on quadratic residues (1976) (65)
- Eisenstein series and Ramanujan-type series for 1/π (2010) (65)
- Reciprocity theorems for dedekind sums and generalizations (1977) (60)
- Asymptotic expansions of certain partial theta functions (2011) (56)
- Generalized Dedekind eta-functions and generalized Dedekind sums (1973) (55)
- On the Hurwitz zeta-function (1972) (54)
- q‐SERIES: THEIR DEVELOPMENT AND APPLICATION IN ANALYSIS, NUMBER THEORY, COMBINATORICS, PHYSICS, AND COMPUTER ALGEBRA (CBMS Regional Conference Series in Mathematics 66) (1987) (54)
- Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory (1975) (51)
- Partition identities and Ramanujan's modular equations (2007) (51)
- Ramanujan’s Formula for ζ(2n + 1) (2017) (50)
- Ramanujan and the Modular j-Invariant (1999) (49)
- Hecke's Theory of Modular Forms and Dirichlet Series (2007) (48)
- Analytic Properties of Arithmetic Sums Arising in the Theory of the Classical Theta-Functions (1984) (48)
- Ramanujan's forty identities for the Rogers-Ramanujan functions (2007) (46)
- Explicit evaluations of the Rogers-Ramanujan continued fraction. (1996) (43)
- Ramanujan's class invariants and cubic continued fraction (1995) (41)
- The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society [ MR1665361 (2000i:11003)] (2001) (40)
- Generalized Eisenstein series and modified Dedekind sums. (1975) (38)
- Dedekind Sums and a Paper of G. H. Hardy (1976) (38)
- Formulas of Ramanujan for the power series coefficients of certain quotients of Eisenstein series (2002) (38)
- Ramanujan's theory of theta-functions (1993) (37)
- Character transformation formulae similar to those for the Dedekind eta-function (1973) (37)
- Sums of Gauss, Eisenstein, Jacobi, Jacobsthal, and Brewer (1979) (36)
- Some Theorems on the Rogers–Ramanujan Continued Fraction in Ramanujan’s Lost Notebook (2000) (36)
- On Ramanujan's Quartic Theory of Elliptic Functions☆ (2001) (35)
- Sixth Order Mock Theta Functions (2007) (34)
- Ramanujan's series for 1/π arising from his cubic and quartic theories of elliptic functions (2008) (34)
- Ramanujan: Essays and Surveys (2001) (34)
- Ramanujan's identities for eta-functions (1992) (33)
- Partition-Theoretic Interpretations of Certain Modular Equations of Schröter, Russell, and Ramanujan (2007) (33)
- Elementary Evaluation of ζ(2n) (1975) (33)
- Chapter 7 of Ramanujan’s second notebook (1981) (32)
- On Eisenstein series with characters and the values of Dirichlet L-functions (1975) (32)
- Eisenstein Series and Approximations to π (2001) (31)
- Finite trigonometric sums and class numbers (2004) (31)
- Sums involving the greatest integer function and Riemann-Stieltjes integration. (1982) (31)
- The Gamma Function and the Hurwitz Zeta-Function (1985) (30)
- The Rogers-Ramanujan continual fraction (1999) (30)
- On Ramanujan’s continued fraction for (²;³)_{∞}/(;³)_{∞} (2002) (30)
- ON THE PARITY OF PARTITION FUNCTIONS (2003) (29)
- A transformation formula involving the gamma and riemann zeta functions in Ramanujan's lost notebook (2009) (28)
- On the Brocard–Ramanujan Diophantine Equation n! + 1 = m2 (2000) (28)
- Periodic Bernoulli Numbers, Summation Formulas and Applications (1975) (28)
- Two new proofs of lerch's functional equation (1972) (28)
- On a secant Dirichlet series and Eichler integrals of Eisenstein series (2014) (27)
- Ramanujan's remarkable product of theta-functions (1997) (27)
- Continued fractions with three limit points (2005) (27)
- On Ramanujan's continued fraction for (q2;q3) ∞(q; q3)∞ (2005) (27)
- New pathways and connections in Number Theory and Analysis motivated by two incorrect claims of Ramanujan (2016) (27)
- A New Identity for (q;q)∞10 with an Application to Ramanujan's Partition Congruence Modulo 11 (2004) (26)
- Integrals associated with Ramanujan and elliptic functions (2016) (26)
- A reciprocity theorem for certain q-series found in Ramanujan’s lost notebook (2007) (25)
- Combinatorial Proofs of Identities in Ramanujan’s Lost Notebook Associated with the Rogers-Fine Identity and False Theta Functions (2003) (25)
- A certain quotient of eta-functions found in Ramanujan’s lost notebook (2002) (25)
- Incomplete elliptic integrals in Ramanujan's lost notebook (2000) (25)
- Ramanujan--for lowbrows (1993) (24)
- Eisenstein Series in Ramanujan's Lost Notebook (2000) (24)
- Cranks and dissections in Ramanujan's lost notebook (2005) (24)
- Ramanujan’s Unpublished Manuscript on the Partition and Tau Functions (2001) (24)
- Chapter 12 of Ramanujan's second notebook: Continued fractions (1985) (24)
- On the average order of a class of arithmetical functions, I (1971) (24)
- ON THE ZEROS OF THE RIEMANN ZETA-FUNCTION (1969) (24)
- Sums of squares and sums of triangular numbers (2006) (23)
- Ramanujan's Explicit Values for the Classical Theta-Function (1995) (23)
- Weighted Divisor Sums and Bessel Function Series (2006) (23)
- A New Class of Theta-Function Identities Originating in Ramanujan′s Notebooks (1994) (22)
- Circle and divisor problems, and double series of Bessel functions (2013) (21)
- A PAGE ON EISENSTEIN SERIES IN RAMANUJAN'S LOST NOTEBOOK (2003) (21)
- Continued fractions : from analytic number theory to constructive approximation : a volume in honor of L.J. Lange : Continued Fractions, From Analytic Number Theory to Constructive Approximation, May 20-23, 1998, University of Missouri-Columbia (1999) (21)
- Integrals of Eisenstein series and derivatives of L-functions (2002) (20)
- An Unpublished Manuscript of Ramanujan on Infinite Series Identities (2013) (20)
- Partition identities arising from theta function identities (2008) (20)
- Ramanujan's Singular Moduli (1997) (19)
- RAMANUJAN'S CONGRUENCES FOR THE PARTITION FUNCTION MODULO 5, 7, AND 11 (2007) (19)
- The Queen of Mathematics (1998) (18)
- Weighted divisor sums and Bessel function series, IV (2012) (18)
- Ramanujan reaches his hand from his grave to snatch your theorems from you (2011) (17)
- Koshliakov's formula and Guinand's formula in Ramanujan's lost notebook (2008) (17)
- On a certain theta-function in a letter of Ramanujan from Fitzroy House (1992) (16)
- What is a q-series? (2010) (16)
- Radicals and units in Ramanujan's work (1998) (16)
- Ramanujan's Eisenstein series and new hypergeometric-like series for 1/pi2 (2009) (16)
- The Circle Problem of Gauss and the Divisor Problem of Dirichlet—Still Unsolved (2018) (15)
- Modular Equations in Ramanujan’s Lost Notebook (2000) (15)
- Extensions of asymptotic expansions from Chapter 15 of Ramanujan's second notebook. (1985) (15)
- Elementary evaluation of $zeta (2n)$ (1975) (14)
- Flowers which we cannot yet see growing in Ramanujan's garden of hypergeometric series, elliptic functions, and q's (2001) (14)
- RAMANUJAN'S ASSOCIATION WITH RADICALS IN INDIA (1997) (14)
- Sums of squares and products of Bessel functions (2017) (14)
- Chapter 6 of Ramanujan’s second notebook (1983) (14)
- The Voronoï summation formula (1972) (14)
- Well-Poised Series (2009) (14)
- Commentary on an unpublished lecture by G. N. Watson on solving the quintic (2002) (14)
- Ramanujan's short unpublished manuscript on integrals and series related to Euler's constant (2000) (14)
- Hypergeometric Series, II (1989) (13)
- DETERMINATIONS OF ANALOGUES OF GAUSS SUMS AND OTHER TRIGONOMETRIC SUMS (2005) (13)
- PROOFS OF CONJECTURES OF SANDON AND ZANELLO ON COLORED PARTITION IDENTITIES (2014) (12)
- New identities for the Rogers-Ramanujan functions (2005) (12)
- ... And Free Lunch for All. A Review of Bruce C Berndt's Ramanujan's Notebooks, Parts I - V. (2000) (12)
- Character analogues of theorems of Ramanujan, Koshliakov and Guinand (2011) (12)
- Rudiments of the theory of the gamma function. (1976) (12)
- Questionable claims found in Ramanujan's lost notebook (2008) (11)
- Fragments by Ramanujan on Lambert series (1999) (11)
- Rankin memorial issues (2003) (11)
- Ramanujan’s Elementary Method in Partition Congruences (2012) (11)
- Analytic Number Theory : Proceedings of a Conference In Honor of Heini Halberstam Volume 1 (1996) (11)
- Your hit parade: The top ten most fascinating formulas in Ramanujan's lost notebook (2008) (11)
- Identities for Partitions with Distinct Colors (2015) (11)
- On the power series coefficients of certain quotients of Eisenstein series (2005) (11)
- New theorems on the parity of partition functions (2004) (11)
- Chapter 15 of Ramanujan's Second Notebook: Part 2, Modular forms (1986) (10)
- FOUR IDENTITIES FOR THIRD ORDER MOCK THETA FUNCTIONS (2018) (10)
- Corrigendum to the paper: ``Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory'' [Acta Arith. bf 28 (1975/76), no. 1, 23--68; MR bf 52 5586] (1975) (10)
- Ramanujan’s Contributions to Eisenstein Series, Especially in His Lost Notebook (2002) (10)
- On the zeros of a class of Dirichlet series I (1970) (10)
- Partitions into kth powers of terms in an arithmetic progression (2018) (9)
- Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi (2011) (9)
- THE QUARTERLY REPORTS OF S. RAMANUJAN (1983) (9)
- The Circle and Divisor Problems, and Ramanujan's Contributions through Bessel Function Series (2013) (9)
- On Gaussian sums and other exponential sums with periodic coefficients (1973) (9)
- Zero sums of the Legendre symbol (1974) (9)
- An integral of Dedekind eta-functions in Ramanujan's lost notebook (2002) (9)
- The Books Studied by Ramanujan in India (2000) (9)
- Weighted divisor sums and Bessel function series, IV (2012) (9)
- Ramanujan’s Theory of Divergent Series (1985) (8)
- An identity for the Dedekind eta‐function involving two independent complex variables (2007) (8)
- Ramanujan's Quarterly Reports (1984) (8)
- Chapter 9 of Ramanujan's Second Notebook: Infinite Series Identities, Transformations, and Evaluations (1983) (8)
- The number of zeros of the Dedekind zeta-function on the critical line (1971) (8)
- Ramanujan's Formula for $\zeta(2n+1)$ (2017) (7)
- An Overview of Ramanujan's Notebooks (1998) (7)
- A remarkable identity found in Ramanujan's third notebook (1992) (7)
- Generalised Dirichlet series and Hecke's functional equation (1967) (7)
- Ramanujan's modular equations of ``large'' prime degree (1987) (7)
- Cranks—really, the final problem (2010) (7)
- Notes on Ramanujan's singular moduli (1999) (7)
- Congruences for the coefficients of quotients of Eisenstein series (2002) (7)
- Ramanujan's class invariants with applications to the values of $q$-continued fractions and theta functions (1997) (7)
- Asymptotic Formulas for Two Continued Fractions in Ramanujan's Lost Notebook (2002) (7)
- Arithmetical identities and Hecke's functional equation (1969) (6)
- A quasi-theta product in Ramanujan's lost notebook (2003) (6)
- A New Method in Arithmetical Functions and Contour Integration (1973) (6)
- A generalization of a theorem of Gauss on sums involving $[x]$ (1975) (6)
- A class of identities associated with Dirichlet series satisfying Hecke’s functional equation (2021) (6)
- Ramanujan and Cranks (2005) (6)
- Chapter 13 of Ramanujan's second notebook: integrals and asymptotic expansions (1984) (6)
- On the Generalized Rogers–Ramanujan Continued Fraction (2003) (6)
- Theorems on partitions from a page in Ramanujan's lost notebook (2003) (6)
- Logarithmic means and double series of Bessel functions (2015) (6)
- Diophantine approximation of the exponential function and Sondowʼs Conjecture (2013) (6)
- Some elegant approximations and asymptotic formulass of Ramanujan (1991) (6)
- Solving Ramanujan's differential equations for Eisenstein series via a first order Riccati equation (2007) (5)
- A new proof of the reciprocity theorem for Dedekind sums. (1974) (5)
- On the Transformation Formula for the Dedekind Eta-Function (2001) (5)
- Corrigendum to “The determination of Gauss sums” (1982) (5)
- Two entries on bilateral hypergeometric series in Ramanujan's lost notebook (2006) (5)
- An elementary proof of some character sum identities of Apostol (1973) (5)
- q-Gauss summation via Ramanujan and combinatorics (2004) (4)
- Two Dirichlet series evaluations found on page 196 of Ramanujan's Lost Notebook (2012) (4)
- On the average order of some arithmetical functions (1970) (4)
- THE REMAINING 40% OF RAMANUJAN'S LOST NOTEBOOK (Number Theory and its Applications) (1998) (4)
- Ramanujan's ``mixed'' modular equations (1986) (4)
- The final problem: an identity from Ramanujan's lost notebook (2019) (4)
- A proof of the general theta transformation formula (2010) (4)
- Analytic number theory : proceedings of a conference in honor of Paul T. Bateman (1990) (4)
- Remarks on some of Ramanujan's number theoretical discoveries found in his second notebook (1985) (4)
- Dirichlet $L$-functions, elliptic curves, hypergeometric functions, and rational approximation with partial sums of power series (2013) (4)
- An arithmetic Poisson formula (1982) (4)
- Sums Related to the Harmonic Series or the Inverse Tangent Function (1985) (4)
- An integral functional equation of Ramanujan related to the dilogarithm (1990) (4)
- On a theorem of A. I. Popov on sums of squares (2016) (4)
- Two General Series Identities Involving Modified Bessel Functions and a Class of Arithmetical Functions (2022) (3)
- The problems solved by Ramanujan in the Journal of the Indian Mathematical Society (2002) (3)
- On Rademacher's multiplier system for the classical theta-function (1994) (3)
- Chapter 5 Ramanujan's second notebook (1981) (3)
- An Integral Analogue of Theta Functions and Gauss Sums in Ramanujan's Lost Notebook (2009) (3)
- On the average order of ideal functions and other arithmetical functions (1970) (3)
- Ramanujan's inversion formulas for the lemniscate and allied functions (1991) (3)
- Analogues of Koshliakov's formula (2014) (3)
- Ramanujan, His Lost Notebook, Its Importance (2020) (3)
- Two remarkable doubly exponential series transformations of Ramanujan (1994) (3)
- Combinatorial Analysis and Series Inversions (1985) (3)
- The evaluation of infinite series by contour integration (1973) (3)
- A new class of Bessel function integrals (1977) (3)
- The reckoning of certain quartic and octic Gauss sums (1977) (3)
- The Chief Accountant and Mathematical Friend of Ramanujan—S. Narayana Aiyar (2011) (3)
- Identities involving the coe cients of a class of Dirichlet series (1969) (3)
- A fragment on Euler's constant in Ramanujan's lost notebook (2008) (3)
- A note on the number of integral ideals of bounded norm in a quadratic number field (1969) (2)
- Infinite Series Identities, Transformations, and Evaluations (1985) (2)
- The functional equation of some Dirichlet series. II (1971) (2)
- Ramanujan at elementary levels: glimpses (2016) (2)
- THE CIRCLE PROBLEM AND DOUBLE SERIES OF BESSEL FUNCTIONS (2014) (2)
- Ramanujan's formulas for Eisenstein series (1989) (2)
- Some integrals in Ramanujan’s lost notebook (2004) (2)
- The Life and Work of R.A. Rankin (1915–2001) (2003) (2)
- On sums of powers in Ramanujan's lost notebook (2011) (2)
- A reciprocity theorem for certain hypergeometric series (2009) (2)
- Erratum to: A pilgrimage (1986) (2)
- Dedekind sums and class numbers (1977) (2)
- Generalizations of the Andrews–Yee identities associated with the mock theta functions ! ( q ) and (cid:2) ( q ) (2021) (2)
- Asymptotic expansion of a series of Ramanujan (1992) (2)
- The entries in Chapter 9 of Ramanujan’s Second Notebook (1983) (2)
- A Bessel Function Summation (1976) (2)
- Introduction to Ramanujan's modular equations (1988) (2)
- EULER PRODUCTS IN RAMANUJAN'S LOST NOTEBOOK (2013) (2)
- An overview of Ramanujan’s notebooks [redacted] (2001) (2)
- Explicit Values for Ramanujan's Theta Function ϕ(q) (2021) (2)
- Q-series with applications to combinatorics, number theory, and physics : a conference on q-series with applications to combinatorics, number theory, and physics, October 26-28, 2000, University of Illinois (2001) (2)
- Two Exams Taken by Ramanujan in India (2004) (2)
- Some asymptotic formulas for $q$-series found in Ramanujan's third notebook and ``lost notebook'' (1990) (2)
- Diophantine approximation with partial sums of power series (2013) (2)
- Five formulas of Ramanujan arising from Eisenstein series (1995) (2)
- The evaluation of character series by contour integration (1972) (2)
- Ramanujan’s Theory of Prime Numbers (1994) (2)
- Ramanujan's modular equations of degrees $7$ and $11$ (1987) (2)
- Integrals and Asymptotic Expansions (1989) (1)
- A Double Summation (1973) (1)
- Eulerian Polynomials and Numbers, Bernoulli Numbers, and the Riemann Zeta-Function (1985) (1)
- An integral of Dedekind An integral of Dedekind An integral of Dedekind An integral of Dedekind eta-functions in Ramanujans lost notebook (2002) (1)
- The Jacobian Elliptic Functions (1991) (1)
- A new proof of the functional equation of Dirichlet $L$-functions (1973) (1)
- Balanced derivatives, identities, and bounds for trigonometric and Bessel series (2021) (1)
- Ramanujan and the theory of prime numbers (1989) (1)
- Integer Partitions, by George E. Andrews and Kimmo Eriksson, Cambridge University Press 2004, 152pp., £15.99/$24.99 (paperback); £40.00/$70.00 (hardback) (2006) (1)
- Integrals associated with Ramanujan and elliptic functions (2016) (1)
- Ramanujan and Koshliakov Meet Abel and Plana (2021) (1)
- Surveys in number theory : papers from the Milennial Confrerence on Number Theory (2002) (1)
- Ramanujan—100 years old (fashioned) or 100 years new (fangled)? (1988) (1)
- The Appearance of H.F. Baker and E.W. Hobson in “The Man Who Knew Infinity” (2016) (1)
- Half Gauss sums (1980) (1)
- The Continuing Mystery (2018) (1)
- ON RAMANUJAN’S CONTINUED FRACTION FOR (q; q)∞/(q; q)∞ (2003) (1)
- The Evaluation of Certain Classes of Nonabsolutely Convergent Double Series (1975) (1)
- Highly Composite Numbers (2012) (1)
- A Survey on Eisenstein Series in Ramanujan's Lost Notebook (解析的整数論の新しい展開 研究集会報告集) (2002) (1)
- A problem in diophantine approximation found in Ramanujan’s lost notebook (2013) (1)
- Identities for Logarithmic Means: A Survey (2015) (1)
- A Preliminary Version of Ramanujan’s Paper “On the Product \(\prod\limits _{n=0}^{\infty }\left [1 +{ \left ( \tfrac{x} {a+nd}\right )}^{3}\right ]\)” (2013) (1)
- On the zeros of a class of Dirichlet series II (1970) (0)
- The legacy of Srinivasa Ramanujan : proceedings of an international conference in celebration of the 125th anniversary of Ramanujan's birth : University of Delhi, 17-22 December 2012 (2013) (0)
- A Partial Manuscript Connected with Ramanujan’s Paper “Some Definite Integrals” (2013) (0)
- The notebooks of Srinivasa Ramanujan (1988) (0)
- The case λ > 2 (2007) (0)
- Fifth Order Mock Theta Functions: Elementary Identities (2018) (0)
- An Empirical Study of the Rogers-Ramanujan Identities (2005) (0)
- A short biography of S. Narayana Iyer (2001) (0)
- A Partial Manuscript on Fourier and Laplace Transforms (2013) (0)
- Applications of the primary theorem of Chapter 5 (2006) (0)
- Two-parameter identities for divisor sums in algebraic number fields (2021) (0)
- Reviews (2019) (0)
- Asymptotic Formulas for Continued Fractions (2005) (0)
- Sums of Powers, Bernoulli Numbers, and the Gamma Function (1985) (0)
- Asymptotic Estimates for the Fourier Transform on KY”, n 3 2 (2003) (0)
- Ramanujan’s Cubic Analogue of the Classical Ramanujan–Weber Class Invariants (2009) (0)
- Theta Function Identities (2009) (0)
- Asymptotic Expansions and Modular Forms (1989) (0)
- Problems in Diophantine Approximation (2013) (0)
- The Influence of Carr’s Synopsis on Ramanujan (2002) (0)
- The Borweins, indeed, have helped us to find the right roads. (2016) (0)
- J an 2 01 7 Ramanujan ’ s Formula for ζ ( 2 n + 1 ) (2017) (0)
- Koshliakov’s Formula and Guinand’s Formula (2013) (0)
- Integrals of Theta Functions (2005) (0)
- Theorems about the Partition Function on Pages 189 and 182 (2012) (0)
- The Sears– Thomae Transformation (2009) (0)
- Miscellaneous Results in the First Notebook (1998) (0)
- The Heine Transformation (2009) (0)
- S. Janaki Ammal (Mrs. Ramanujan) (2001) (0)
- Ramanujan is ill (1995) (0)
- Analogues of the Gamma Function (1985) (0)
- Eisenstein Series and Modular Equations (2009) (0)
- Certain Integrals Arising from Ramanujan's Notebooks (2015) (0)
- Theorems Featuring the Gamma Function (2013) (0)
- Generalizations of the Andrews–Yee identities associated with the mock theta functions $$\omega (q)$$ and $$\nu (q)$$ (2021) (0)
- The Legacy of Dick Askey (1933–2019) (2022) (0)
- Variations on the Rogers-Ramanujan continued fraction in Ramanujan's notebooks (1989) (0)
- HIGHER MATHEMATICS FROM AN ELEMENTARY POINT OF VIEW (1984) (0)
- Preface (2016) (0)
- Ramanujan returns to India (1995) (0)
- Modified Bessel Functions in Analytic Number Theory (2023) (0)
- Other q-continued Fractions (2005) (0)
- Class Invariants and Singular Moduli (1998) (0)
- Least positive residues and the law of quadratic reciprocity (2017) (0)
- Elementary Problems: E3391-E3396 (1990) (0)
- Modular Equations of Higher and Composite Degrees (1991) (0)
- A Fragment on the Rogers-Ramanujan and Cubic Continued Fractions (2005) (0)
- Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi (2012) (0)
- Two Identities Involving a Mordell Integral and Appell–Lerch Sums (2018) (0)
- Identities Related to the Riemann Zeta Function and Periodic Zeta Functions (2013) (0)
- Ramanujan in Madras (1995) (0)
- A Preliminary Version of Ramanujan’s Paper “On the Integral $$\int _{0}^{x}\frac{{\tan }^{-1}t} {t} dt$$” (2013) (0)
- Tenth Order Mock Theta Functions: Part III, Identities for χ 10 ( q ), X 10 ( q ) (2018) (0)
- Congruences for () and () (2006) (0)
- A brief biography of Ramanujan (1995) (0)
- Miscellaneous Results in Analysis (2013) (0)
- Rogers-Ramanujan-Slater Type Identities (2005) (0)
- Partitions into kth powers of terms in an arithmetic progression (2018) (0)
- The four photographs of Ramanujan (2001) (0)
- Elementary and Miscellaneous Analysis (1994) (0)
- Proofs of McIntosh's conjecture on Franel integrals and two generalizations (2022) (0)
- Two Partial Unpublished Manuscripts on Sums Involving Primes (2013) (0)
- Rogers-Ramanujan Continued Fraction and Its Modular Properties (2005) (0)
- Ramanujan's Beautiful Integrals (2021) (0)
- Title A SURVEY ON EISENSTEIN SERIES IN RAMANUJAN'S LOST NOTEBOOK (New Aspects of Analytic Number Theory) (2018) (0)
- Ramanujan’s series for 1/π: A survey (2009) (2016) (0)
- Number theory and modular forms : papers in memory of Robert A. Rankin (2003) (0)
- A recently discovered letter giving Ramanujan’s examination scores (2001) (0)
- PROOFS OF MCINTOSH’S CONJECTURE ON FRANEL INTEGRALS AND TWO EXTENSIVE GENERALIZATIONS (2022) (0)
- Fundamental Properties of Elliptic Functions (1991) (0)
- Values of Theta—Functions (1998) (0)
- Double Series of Bessel Functions and the Circle and Divisor Problems (2013) (0)
- Ramanujan’s papers and manuscripts (1995) (0)
- Preparing to go to England (1995) (0)
- Conversation “I didn’t understand his work, but I knew his worth” (2001) (0)
- Ranks and Cranks, Part III (2012) (0)
- Theta-Functions and Modular Equations (1994) (0)
- Partial Fraction Expansions (1994) (0)
- PARTITION IDENTITIES INSPIRED BY RAMANUJAN (2014) (0)
- An overview of Ramanujan's notebooks [ MR1672414 (99k:01032)] (2001) (0)
- Living with Ramanujan for 40 years (2019) (0)
- ABSTRACTS OF ALL TALKS (2005) (0)
- SUMMATION VIA RAMANUJAN AND COMBINATORICS (2004) (0)
- Two Letters on Eisenstein Series Written from Matlock House (2009) (0)
- Combinatory Analysis 2018: In Honor of George Andrews’ 80th Birthday (2019) (0)
- INFINITELY MANY ZEROS OF ζ ( s ) LIE ON σ = 1 2 (2013) (0)
- The Rogers-Ramanujan Continued Fraction and Its Connections with Partitions and Lambert Series (2005) (0)
- Finite trigonometric sums arising from Ramanujan's theta functions (2022) (0)
- Fifth Order Mock Theta Functions: Proof of the Mock Theta Conjectures (2018) (0)
- Modular Equations and Theta—Function Identities in Notebook 1 (1998) (0)
- Exercises in Number Theory. By D. P. Parent. (1986) (0)
- Incomplete Elliptic Integrals (2005) (0)
- Discarded fragments from Ramanujan's papers (2012) (0)
- Recent Work on Mock Theta Functions (2018) (0)
- Provenance of letters (1995) (0)
- A Strange, Enigmatic Partial Manuscript (2013) (0)
- After his death (1995) (0)
- A problem in diophantine approximation found in Ramanujan’s lost notebook (2012) (0)
- The Final Problem: A Series Identity from the Lost Notebook (2020) (0)
- π related developments since 1988 (2001) (0)
- Transformation Formulas: 10th Order Mock Theta Functions (2018) (0)
- Iterates of the Exponential Function and an Ingenious Formal Technique (1985) (0)
- Fragments on Lambert Series (2005) (0)
- The Rogers-Fine Identity (2005) (0)
- Finite Rogers-Ramanujan Continued Fractions (2005) (0)
- Program Committee Local Committee Special Session Organizers Wednesday 28 (2005) (0)
- On a secant Dirichlet series and Eichler integrals of Eisenstein series (2016) (0)
- RAMANUJAN’S EARLIER NOTEBOOKS AND HIS LOST NOTEBOOK (2014) (0)
- The connection between hypergeometric functions and theta functions (2006) (0)
- Bailey’s Lemma and Theta Expansions (2009) (0)
- Series Representable in Terms of Eisenstein Series (2009) (0)
- TWO DIRICHLET SERIES FOUND ON PAGE 196 OF RAMANUJAN ’ S LOST NOTEBOOK (2011) (0)
- The De Morgan Medal (0)
- Number Theory for the Millennium III (2023) (0)
- The Mock Theta Conjectures: Equivalence (2018) (0)
- Tenth Order Mock Theta Functions: Part IV (2018) (0)
- A theorem of Ramanujan on certain alternating series (1993) (0)
- Erratum: “On the zeros of the Riemann zeta-function” (1970) (0)
- Finite and infinite Rogers-Ramanujan continued fractions in Ramanujan's lost notebook (2015) (0)
- A pilgrimage (1986) (0)
- Bochner's generalization of the main correspondence theorem of Hecke, and related results (2007) (0)
- Number Theory and Modular Forms (2003) (0)
- Congruences for Generalized Tau Functions on Page 178 (2012) (0)
- Lecture given by B. M. Wilson, University of Leeds, May, 1927 (2013) (0)
- Miscellaneous Results on Eisenstein Series (2009) (0)
- Identities for Partitions with Distinct Colors (2015) (0)
- The books studied by Ramanujan in India [ MR1786233 (2002b:01036)] (2001) (0)
- Hadamard Products for Two q-Series (2005) (0)
- Approximations and Asymptotic Expansions (1998) (0)
- L. J. Lange on his 70th birthday (1999) (0)
- Working mostly in isolation, Ramanujan noted striking and sometimes still unproved results in series, special functions and number theory. (2016) (0)
- The main correspondence theorem (2007) (0)
- Ramanujan’s first two letters to Hardy and Hardy’s responses (1995) (0)
- Miscellaneous Results on Elliptic Functions and Theta Functions (2009) (0)
- Commentary on and Corrections to the First Four Volumes (2018) (0)
- A fundamental region (2007) (0)
- CONGRUENCES FOR FIVE TRIANGLES (2016) (0)
- q-Series and Theta-Functions (1991) (0)
- Identities equivalent to the functional equation and to the modular relation (2007) (0)
- Integral Analogues of Theta Functions and Gauss Sums (2013) (0)
- Inversion Formulas for the Lemniscate and Allied Functions (1994) (0)
- Ramanujan at Cambridge (1995) (0)
- Modular Equations of Degrees 3, 5, and 7 and Associated Theta-Function Identities (1991) (0)
- A multi-variable theta product (2002) (0)
- Third Order Mock Theta Functions: Partial Fraction Expansions (2018) (0)
- Formulas for the Power Series Coefficients of Certain Quotients of Eisenstein Series (2009) (0)
- On a conjecture of (2012) (0)
- Advanced Problems: 6368-6373 (1981) (0)
- Maihemalik Dedekind Sums and Class Numbers (2005) (0)
- University lectures in Madras (2001) (0)
- Two Partial Manuscripts on Euler’s Constant γ (2013) (0)
- The first wo formulas , ( 1 . 2 ) and ( 1 . 3 ) , appeared in the Walt Disney film High School Musical , starring (2015) (0)
- Functional Equations for Products of Mellin Transforms (2013) (0)
- Elementary Problems: E2755-E2760 (1979) (0)
- A continued fraction from Ramanujan’s lost notebook (2005) (0)
- Tenth Order Mock Theta Functions: Part I, The First Four Identities (2018) (0)
- Ramanujan’s Last Letter to Hardy (2018) (0)
- Infinite Integrals of q-Products (2005) (0)
- An identity for certain Dirichlet series (1968) (0)

This paper list is powered by the following services:

Bruce C. Berndt is affiliated with the following schools:

This website uses cookies to enhance the user experience. Read the Privacy Policy for more.