Bob Vaughan

Q: What Schools Are Affiliated With Bob Vaughan

Bob Vaughan is affiliated with the following schools: University of Michigan, Pennsylvania State University, University of Surrey

Bob Vaughan's AcademicInfluence.com Rankings

Bob Vaughan

Mathematics

#1520

World Rank

#2475

Historical Rank

Measure Theory

#1778

World Rank

#2178

Historical Rank

mathematics Degrees

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Mathematics

Why Is Bob Vaughan Influential?

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According to Wikipedia, Robert Charles "Bob" Vaughan FRS is a British mathematician, working in the field of analytic number theory. Life Since 1999 he has been Professor at Pennsylvania State University, and since 1990 Fellow of the Royal Society. He did his PhD at the University of London under supervision of Theodor Estermann. He supervised Trevor Wooley's PhD.

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Bob Vaughan's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Multiplicative Number Theory I: Classical Theory (2006) (795)
The Hardy-Littlewood Method (1981) (667)
Hilbert’s inequality (1974) (308)
The large sieve (1973) (185)
A new iterative method in Waring's problem (1989) (166)
The exceptional set in Goldbach''s problem (1975) (165)
An elementary method in prime number theory (1980) (122)
The Hardy–Littlewood method: Frontmatter (1997) (116)
Exponential sums with multiplicative coefficients (1977) (93)
Sums of Three Cubes (1985) (88)
Diophantine approximation on planar curves: the convergence theory (2006) (85)
On Waring's Problem for Smaller Exponents (1986) (82)
Waring's problem: A survey (2002) (80)
Diophantine Approximation by Prime Numbers, III (1974) (73)
Further improvements in Waring's problem (1995) (71)
On the distribution of αp modulo 1 (1977) (70)
The Hardy–Littlewood method: Bibliography (1997) (62)
On the fractional parts of $x/n$ and related sequences. II (1977) (60)
Mean Value Theorems in Prime Number Theory (1975) (58)
The k -dimensional Duffin and Schaeffer conjecture (1990) (58)
Extreme values of Dirichlet L-functions at 1 (1999) (53)
Multiplicative Number Theory I: Zeros (2006) (52)
On the distribution of reduced residues (1986) (52)
Diophantine approximation on planar curves and the distribution of rational points (with an appendix "Sum of two squares near perfect squares" by R.C. Vaughan) (2007) (49)
Mean values of multiplicative functions (2002) (49)
On a certain nonary cubic form and related equations (1995) (47)
On sums of primes (1983) (42)
Bounds for the coefficients of cyclotomic polynomials. (1975) (42)
The Estimation of Complete Exponential Sums (1985) (41)
On waring's problem : some refinements (1991) (41)
Some applications of Montgomery's sieve (1973) (39)
The Hardy–Littlewood method: Preface to second edition (1997) (38)
NUMBER THEORY FOR THE MILLENNIUM III (2002) (36)
Sieve Methods, Exponential Sums, and their Applications in Number Theory: On the Montgomery-Hooley Asymptotic Formula (1997) (34)
On Waring's problem for smaller exponents. II (1986) (33)
Further improvements in Waring's problem, IV: Higher powers (2000) (33)
On the fractional parts of x/n and related sequences. III (2018) (32)
Diophantine approximation on manifolds and the distribution of rational points: contributions to the convergence theory (2015) (31)
On Waring's Problem for Cubes II (1989) (31)
On a variance associated with the distribution of primes in arithmetic progressions (2001) (30)
On Goldbach's problem (1972) (28)
ERROR TERMS IN ADDITIVE PRIME NUMBER THEORY (1973) (27)
On a problem of Erds, Straus and Schinzel (1970) (26)
Analytic number theory : essays in honour of Klaus Roth (2009) (25)
Multiplicative Number Theory I: Contents (2006) (24)
Squares: Additive questions and partitions (2015) (24)
ON A NEW METHOD OF ANALYSIS AND ITS APPLICATIONS (A Volume in Pure and Applied Mathematics: A Wiley‐Interscience Series of Texts, Monographs, and Tracts) (1985) (24)
On the exponential sum over k–free numbers (1998) (24)
On the number of partitions into primes (2008) (23)
The divisor function on residue classes I (2018) (23)
The Virginia Statute for Religious Freedom : its evolution and consequences in American history (1990) (23)
A New Iterative Method in Waring's Problem II (1989) (22)
Inhomogeneous Diophantine approximation on planar curves (2009) (22)
Further improvements in Waring’s problem, II: Sixth powers (1994) (22)
On a variance associated with the distribution of general sequences in arithmetic progressions. I (1998) (21)
Bounds for the R-th Coefficients of Cyclotomic Polynomials (1974) (19)
On the eigenvalues of Redheffer's matrix, II (1996) (19)
Mean Values of Character Sums (1979) (18)
A special case of Vinogradov's mean value theorem (1997) (18)
On Waring's problem for sixth powers (1986) (18)
On Sums of Mixed Powers (1971) (17)
A Tribute to Paul Erdős: On the Erdős–Fuchs theorems (1990) (17)
A Variance for k‐Free Numbers in Arithmetic Progressions (2005) (16)
A Ternary Additive Problem (1980) (15)
On the addition of sequences of integers (1972) (15)
The L1 mean of Exponential Sums over Primes (1988) (15)
ON WARING'S PROBLEM: ONE SQUARE AND FIVE CUBES (1986) (14)
Inefficiency in Packing Squares with Unit Squares (1978) (13)
Further improvements in Waring’s problem. Ill Eighth powers (1993) (13)
On the order of magnitude of Jacobsthal's function (1977) (12)
DIOPHANTINE APPROXIMATION ON MANIFOLDS AND LOWER BOUNDS FOR HAUSDORFF DIMENSION (2017) (12)
On the Representation of Numbers as Sums of Powers of Natural Numbers (1970) (11)
On the estimation of Schnirelman's constant. (1977) (11)
On generating functions in additive number theory, II: lower-order terms and applications to PDEs (2020) (11)
Mean Value Theorems for Binary Egyptian Fractions (2011) (11)
Homogeneous additive equations and Waring's problem (1977) (10)
On Waring's problem for cubes. (1986) (10)
The order of magnitude of the mth coefficients of cyclotomic polynomials (1985) (10)
On the Distribution of Generating Functions (1998) (9)
AREA, LATTICE POINTS, AND EXPONENTIAL SUMS (LMS Monographs: New Series 13) By M. N. Huxley: 494 pp., £85.00, LMS Members' price £63.75, ISBN 0 19 853466 3 (Clarendon Press, 1996). (1998) (9)
A survey of recent work in additive prime number theory. (1974) (9)
Moments for primes in arithmetic progressions, I (2003) (9)
Zeros of Dirichlet series (2015) (8)
Waring's problem for Beatty sequences and a local to global principle (2014) (8)
A remark on the divisor function d(n) (1973) (7)
On Pairs of Additive Cubic Equations (1977) (7)
Diophantine approximation on curves and the distribution of rational points: divergence theory (2018) (6)
Mean value theorems for binary Egyptian fractions II (2011) (6)
On a variance associated with the distribution of general sequences in arithmetic progressions. II (1998) (6)
On the exceptional set for binary Egyptian fractions (2011) (5)
Goldbach's Conjectures: A Historical Perspective (2016) (5)
The asymptotic formula in Waring’s problem: Higher order expansions (2013) (5)
Ivan Matveevich Vinogradov (1985) (5)
The general Goldbach problem with Beatty primes (2014) (4)
A Note on Šnirel'man's Approach to Goldbach's Problem (1976) (4)
Integer points on elliptic curves (2014) (4)
The use in additive number theory of numbers without large prime factors (1993) (4)
A Note on Šnirel'man's Approach to Goldbach's Problem (1976) (4)
On the Number of Solutions of the Equation P = a +n1 …nk with a = p ⩾ x (1972) (3)
A Montgomery–Hooley Theorem for sums of two cubes (2021) (3)
ON SOME QUESTIONS OF PARTITIO NUMERORUM: TRES CUBI (2020) (3)
Adventures in arithmetick, or: How to make good use of a fourier transform (1987) (3)
The Hardy–Littlewood method: Notation (1997) (3)
The $k$-dimensional Duffin and Schaeffer conjecture (1989) (3)
Theorem with applications in coding and matching problems (1990) (2)
On sigma-PHI numbers (2001) (2)
Hardy's legacy to number theory (1998) (2)
Diophantine approximation on curves and the distribution of rational points: Contributions to the divergence theory (2021) (2)
The divisor function on residue classes III (2020) (2)
Multiplicative Number Theory I: List of notation (2006) (2)
A New Perspective: Southern Women's Cultural History from the Civil War to Civil Rights. (1991) (2)
Bending of uniformly loaded column-supported flat plates (1967) (2)
Determination of elastic moments in flat-plate and lift-slab structures by the moiré method (1968) (2)
On the Number of Solutions of the Equation P +n1 ..nk = N (1973) (2)
Ivan Matveevich Vinogradov, 14 September 1891 - 20 March 1983 (1985) (1)
An Analytic Inequality (1983) (1)
Density of positive diagonal binary quadratic forms (2020) (1)
The Bombieri-Vinogradov theorem (2019) (1)
A mean value theorem for cubic fields (2003) (1)
IN MEMORIAM KLAUS FRIEDRICH ROTH 1925–2015 (2017) (1)
On generating functions in additive number theory, II: lower-order terms and applications to PDEs (2020) (1)
The Bombieri-Vinogradov theorem (2019) (1)
The Hardy–Littlewood method: Homogeneous equations and Birch's theorem (1997) (0)
The "Discretionary-Function" Exception of the Federal Tort Claims Act: Some Reflections on Sovereign Immunity (1957) (0)
Multiplicative Number Theory I: Bernoulli numbers and the Euler–MacLaurin summation formula (2006) (0)
3 0 D ec 2 02 0 A Study on Erdős-Straus conjecture on Diophantine equation 4 n = 1 x + 1 y + 1 z ∗ (2021) (0)
Multiplicative Number Theory I: Applications of the Prime Number Theorem (2006) (0)
The Hardy–Littlewood method: Introduction and historical background (1997) (0)
Multiplicative Number Theory I: Primitive characters and Gauss sums (2006) (0)
THE LANGUAGE OF ANALOGY AND RELIGIOUS EDUCATION (1967) (0)
More information 1 Dirichlet series : I 1 . 1 Generating functions and asymptotics (2011) (0)
Multiplicative Number Theory I: Topics in harmonic analysis (2006) (0)
Comments Concerning Examination and Evaluation of Titles to Real Property in Virginia (1957) (0)
Book Review: Additive number theory of polynomials over a finite field (1993) (0)
Multiplicative Number Theory I: Preface (2006) (0)
The Least Number with Prescribed Legendre Symbols (2016) (0)
Vinogradov's methods (1997) (0)
A generalised divisor problem (2001) (0)
Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences: 356 (1738) (1998) (0)
House Room C General Assembly Building Richmond, Virginia (2011) (0)
Workshop: Analytic Number Theory Table of Contents (2014) (0)
Multiplicative Number Theory I: Oscillations of error terms (2006) (0)
Multiplicative Number Theory I: Primes in arithmetic progressions: II (2006) (0)
Multiplicative Number Theory I: The gamma function (2006) (0)
The Hardy–Littlewood method: The major arcs in Waring's problem (1997) (0)
The Hardy–Littlewood method: A ternary additive problem (1997) (0)
Multiplicative Number Theory I: The Prime Number Theorem (2006) (0)
The Hardy–Littlewood method: Davenport's methods (1997) (0)
Multiplicative Number Theory I: Conditional estimates (2006) (0)
Local variation of Euler products (2008) (0)
Klaus Friedrich Roth. 29 October 1925 — 10 November 2015 (2017) (0)
The Hardy–Littlewood method: Diophantine inequalities (1997) (0)
Multiplicative Number Theory I: The elementary theory of arithmetic functions (2006) (0)
Multiplicative Number Theory I: The Riemann–Stieltjes integral (2006) (0)
Study of rational cubic forms via the circle method [ after (2019) (0)
The Hardy–Littlewood method: Vinogradov's upper bound for G ( k ) (1997) (0)
A remark on Freud’s tauberian theorem (1983) (0)
COLLECTED PAPERS OF PAUL TURÁN (1991) (0)
THEORY OF NUMBERS. (1970) (0)
Multiplicative Number Theory I: Principles and first examples of sieve methods (2006) (0)
The Hardy–Littlewood method: Preface (1997) (0)
The Hardy–Littlewood method: Wooley's upper bound for G(k) (1997) (0)
Multiplicative Number Theory I: Analytic properties of the zeta function and L -functions (2006) (0)
Dirichlet series: II (2006) (0)
The Hardy–Littlewood method: Goldbach's problems (1997) (0)
The Hardy–Littlewood method: A theorem of Roth (1997) (0)
Dr. Martin Luther King, Jr. Memorial Commission (2011) (0)
A survey of some important problems in additive number theory (2019) (0)
The Hardy–Littlewood method: The simplest upper bound for G(k) (1997) (0)
The least number with prescribed Legendre symbols and representation by binary quadratic forms of small discriminant (2017) (0)
Corrigendum to “On the number of partitions into primes” (2017) (0)
Multiplicative Number Theory I: Explicit formulæ (2006) (0)
Multiplicative Number Theory I: Further discussion of the Prime Number Theorem (2006) (0)
The Problime Number Theorem (1974) (0)
The general Goldbach problem with Beatty primes (2013) (0)
Sums of two unlike powers in arithmetic progressions (2022) (0)
Corrigendum to “On the number of partitions into primes” (2018) (0)
Recent Work on Waring's Problem (1989) (0)
Multiplicative Number Theory I: Dirichlet series: II (2006) (0)

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Other Resources About Bob Vaughan

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What Schools Are Affiliated With Bob Vaughan?

Bob Vaughan is affiliated with the following schools:

Bob Vaughan's Academic­Influence.com Rankings