# Ken Ono

#7,216

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American mathematician

## Ken Ono's AcademicInfluence.com Rankings

Ken Onomathematics Degrees

Mathematics

#436

World Rank

#872

Historical Rank

#198

USA Rank

Number Theory

#41

World Rank

#64

Historical Rank

#12

USA Rank

Measure Theory

#1894

World Rank

#2309

Historical Rank

#579

USA Rank

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Mathematics

## Ken Ono's Degrees

- Bachelors Mathematics University of Chicago

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## Why Is Ken Ono Influential?

(Suggest an Edit or Addition)According to Wikipedia, Ken Ono is an American mathematician who specializes in number theory, especially in integer partitions, modular forms, umbral moonshine, the Riemann Hypothesis and the fields of interest to Srinivasa Ramanujan. He is the STEM Advisor to the Provost and the Marvin Rosenblum Professor of Mathematics at the University of Virginia.

## Ken Ono's Published Works

### Published Works

- The web of modularity : arithmetic of the coefficients of modular forms and q-series (2003) (799)
- Unearthing the visions of a master: harmonic Maass forms and number theory (2008) (232)
- Distribution of the partition function modulo $m$ (2000) (216)
- Dyson’s ranks and Maass forms (2010) (207)
- Heegner divisors, $L$-functions and harmonic weak Maass forms (2007) (189)
- THE f(q) MOCK THETA FUNCTION CONJECTURE AND PARTITION RANKS (2005) (179)
- Harmonic Maass Forms and Mock Modular Forms: Theory and Applications (2017) (170)
- Defect zero p-blocks for finite simple groups (1996) (167)
- A Gaussian hypergeometric series evaluation and Apéry number congruences (2000) (163)
- -Series with Applications to Combinatorics, Number Theory, and Physics (2001) (152)
- Congruence properties for the partition function (2001) (120)
- Values of Gaussian hypergeometric series (1998) (115)
- Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms (2011) (106)
- Divisibility of Certain Partition Functions by Powers of Primes (1997) (101)
- Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues (2008) (95)
- Non-vanishing of quadratic twists of modular L-functions (1998) (95)
- Ramanujan’s Unpublished Manuscript on the Partition and Tau Functions with Proofs and Commentary (2001) (94)
- The arithmetic of the values of modular functions and the divisors of modular forms (2004) (92)
- MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS (2013) (82)
- Jensen polynomials for the Riemann zeta function and other sequences (2019) (81)
- Eulerian series as modular forms (2007) (79)
- Proof of the umbral moonshine conjecture (2015) (76)
- The spt-function of Andrews (2008) (73)
- q-series identities and values of certain L-functions (2001) (66)
- The f(q) mock theta function conjecture and partition ranks (2006) (65)
- ARITHMETIC PROPERTIES OF COEFFICIENTS OF HALF-INTEGRAL WEIGHT MAASS-POINCARÉ SERIES (2006) (65)
- Parity of the partition function in arithmetic progressions. (1996) (65)
- Gaussian hypergeometric functions and traces of Hecke operators (2004) (64)
- Baxter Algebras and Hopf Algebras (2003) (64)
- Unimodal sequences and quantum and mock modular forms (2012) (63)
- Hilbert class polynomials and traces of singular moduli (2006) (62)
- Fourier coe cients of half-integral weight modular forms modulo (1998) (62)
- Lifting cusp forms to Maass forms with an application to partitions (2007) (61)
- On the representation of integers as sums of triangular numbers (1995) (60)
- Eichler–Shimura theory for mock modular forms (2013) (54)
- Indivisibility of class numbers of imaginary quadratic fields and orders of Tate-Shafarevich groups of elliptic curves with complex multiplication (1999) (52)
- Parity of the Partition Function in Arithmetic Progressions, II (2001) (50)
- RAMANUJAN’S TERNARY QUADRATIC FORM (2004) (49)
- A framework of Rogers–Ramanujan identities and their arithmetic properties (2014) (46)
- Addition and counting: the arithmetic of partitions (2001) (46)
- Maximal Multiplicative Properties of Partitions (2014) (45)
- Arithmetic of singular moduli and class polynomials (2005) (44)
- NONVANISHING OF QUADRATIC TWISTS OF MODULAR L-FUNCTIONS AND APPLICATIONS TO ELLIPTIC CURVES (2001) (42)
- The Chebotarev Density Theorem in Short Intervals and Some Questions of Serre (2001) (42)
- 4-core partitions and class numbers (1997) (42)
- Euler ’ s concordant forms (1996) (41)
- Representations of Integers as Sums of Squares (2002) (41)
- ℓ-Adic properties of the partition function☆☆☆ (2012) (41)
- Fourier coefficients of half-integral weight modular forms modulo ell (1996) (41)
- Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues (2008) (41)
- The 2-Adic Behavior of the Number of Partitions into Distinct Parts (2000) (40)
- Zeta functions of an infinite family of K3 surfaces (2002) (39)
- Prime Power Degree Representations of the Symmetric and Alternating Groups (2001) (38)
- COEFFICIENTS OF HARMONIC MAASS FORMS (2009) (37)
- Arithmetic properties of coefficients of half-integral weight Maass–Poincaré series (2007) (37)
- SO(3)-Donaldson invariants of CP^2 and Mock Theta Functions (2008) (36)
- Reduction of CM elliptic curves and modular function congruences (2005) (35)
- Euler's concordant forms (1996) (35)
- ETA-QUOTIENTS AND ELLIPTIC CURVES (2004) (35)
- Some characters of Kac and Wakimoto and nonholomorphic modular functions (2009) (35)
- Ramanujan’s mock theta functions (2013) (32)
- Weierstrass mock modular forms and elliptic curves (2014) (32)
- Congruences for Frobenius Partitions (1996) (32)
- p-adic coupling of mock modular forms and shadows (2010) (31)
- Theorems and Conjectures Involving Rook Polynomials with Only Real Zeros (1999) (31)
- Indivisibility of Class Numbers of Real Quadratic Fields (1999) (30)
- Congruences for the Andrews spt function (2010) (29)
- Duality involving the mock theta function f(q) (2008) (28)
- Selmer groups of quadratic twists of elliptic curves (1999) (28)
- Class polynomials for nonholomorphic modular functions (2013) (27)
- On Divisors of Modular Forms (2016) (27)
- MODULARITY OF A CERTAIN CALABI-YAU THREEFOLD (2004) (27)
- Linear Relations Between Modular form Coefficients and Non‐Ordinary Primes (2005) (26)
- Congruences and conjectures for the partition function (2001) (26)
- q-series and weight 3/2 Maass forms (2009) (26)
- The arithmetic of Borcherds' exponents (2003) (25)
- Riemann hypothesis for period polynomials of modular forms (2016) (25)
- Eta-quotients and elliptic curves (1997) (24)
- On the positivity of the number of t-core partitions (1994) (23)
- Weierstrass points on X0(p) and supersingular j-invariants (2003) (22)
- Ramanujan's ternary quadratic form (1997) (21)
- 2-ADIC PROPERTIES OF CERTAIN MODULAR FORMS AND THEIR APPLICATIONS TO ARITHMETIC FUNCTIONS (2005) (20)
- ARITHMETIC PROPERTIES OF COEFFICIENTS OF HALF-INTEGRAL WEIGHT MAASS-POINCARÉ SERIES (2006) (20)
- A MOCK THETA FUNCTION FOR THE DELTA-FUNCTION (2008) (20)
- On the Circular Summation of the Eleventh Powers of Ramanujan's Theta Function (1999) (20)
- Classical and Umbral Moonshine: Connections and $p$-adic Properties (2014) (19)
- Coefficients of half-integral weight modular forms (2003) (19)
- COEFFICIENTS OF HALF-INTEGRAL WEIGHT MODULAR FORMS (2004) (18)
- AN ARITHMETIC FORMULA FOR THE PARTITION FUNCTION (2006) (18)
- The partition function in arithmetic progressions (1998) (18)
- Hook Lengths and 3-Cores (2008) (17)
- Variations of Lehmer's Conjecture for Ramanujan's tau-function (2020) (17)
- Hypergeometric generating functions for values of Dirichlet and other L functions (2003) (17)
- A Binomial Coefficient Identity Associated to a Conjecture of Beukers (1998) (17)
- Modularity of a Certain Calabi-Yau Threefold (2000) (17)
- O'Nan moonshine and arithmetic (2017) (17)
- Congruences for partition functions (1996) (16)
- Superlacunary cusp forms (1995) (16)
- A Note on the Number of $t$-Core Partitions (1995) (15)
- Jensen polynomials for the Riemann xi-function (2019) (15)
- Number theoretic properties of Wronskians of Andrews-Gordon series (2005) (15)
- Coefficients of Harmonic Maass Forms (2012) (14)
- Twists of elliptic curves (1997) (14)
- Elements of class groups and Shafarevich-Tate groups of elliptic curves (2003) (14)
- Partition-Theoretic Formulas for Arithmetic Densities (2016) (14)
- A Creative Genius (2016) (14)
- Variants of Lehmer's speculation for newforms (2020) (14)
- Parity of the partition function (2010) (13)
- Pariah moonshine (2017) (13)
- Black holes and class groups (2018) (13)
- Hasse invariants for the Clausen elliptic curves (2013) (13)
- Distributions on partitions arising from Hilbert schemes and hook lengths (2021) (13)
- Zeta-polynomials for modular form periods (2016) (12)
- Congruences for Fourier coefficients of half-integral weight modular forms and special values of L-functions (1996) (12)
- Eichler integrals of Eisenstein series as q-brackets of weighted t-hook functions on partitions (2020) (12)
- A q-SERIES IDENTITY AND THE ARITHMETIC OF HURWITZ ZETA FUNCTIONS (2004) (12)
- The Jack Daniels Problem (2014) (11)
- Explorations in the Theory of Partition Zeta Functions (2016) (11)
- Traces of singular moduli on Hilbert modular surfaces (2005) (11)
- Rankin memorial issues (2003) (11)
- An arithmetic formula for the partition function (2007) (11)
- Rank zero quadratic twists of modular elliptic curves (1996) (11)
- LIFTING ELLIPTIC CUSP FORMS TO MAASS FORMS WITH AN APPLICATION TO PARTITIONS (2006) (10)
- Identities and congruences for Ramanujan’s ω(q) (2010) (10)
- Combinatorics of traces of Hecke operators. (2004) (10)
- Modular Form Congruences and Selmer Groups (2003) (9)
- A Note on the Irreducibility of Hecke Polynomials (1998) (9)
- Turán inequalities for the plane partition function (2022) (9)
- Ramanujan's congruences and Dyson's crank (2005) (9)
- SU(2)-Donaldson invariants of the complex projective plane (2012) (9)
- Rook Theory and t-Cores (1998) (9)
- Arithmetic of certain hypergeometric modular forms (2004) (9)
- Differential operators and harmonic weak Maass forms (2008) (8)
- Moonshine and Donaldson invariants of CP^2 (2012) (8)
- THEOREMS AND CONJECTURES INVOLVING ROOK POLYNOMIALS WITH REAL ROOTS (1997) (8)
- Research in the Mathematical Sciences: a new open access journal (2014) (8)
- Tate-Shafarevich groups of the congruent number elliptic curves (1997) (8)
- Special values of shifted convolution Dirichlet series (2014) (8)
- Shimura sums related to imaginary quadratic fields (1994) (7)
- Mock modular Eisenstein series with Nebentypus (2019) (7)
- MOCK THETA FUNCTIONS , RANKS , AND MAASS FORMS (2007) (7)
- A mod ℓ Atkin–Lehner theorem and applications (2012) (7)
- Odd values of the partition function (1997) (6)
- A NOTE ON THE SHIMURA CORRESPONDENCE AND THE RAMANUJAN τ ( n ) FUNCTION (2004) (6)
- From partitions to Hodge numbers of Hilbert schemes of surfaces (2019) (6)
- ARITHMETIC OF THE PARTITION FUNCTION (6)
- Honoring a Gift from Kumbakonam (2006) (6)
- A q-series identity and the arithmetic of Hurwitz zeta functions (2002) (6)
- HARMONIC MAASS FORMS , MOCK MODULAR FORMS , AND QUANTUM MODULAR FORMS (2012) (6)
- Class numbers and self-conjugate 7-cores (2019) (6)
- Congruence Properties of Values of L-Functions and Applications (1999) (6)
- RANK ZERO QUADRATIC TWISTS OF MODULAR ELLIPTIC CURVES (2004) (5)
- Mock Theta Functions Ranks and Maass Forms (2008) (5)
- CM Evaluations of the Goswami-Sun Series (2018) (5)
- Elliptic curves and lower bounds for class numbers (2020) (5)
- Moonshine for M24 and Donaldson Invariants of Cp (2013) (5)
- On Witten’s Extremal Partition Functions (2018) (5)
- Corrigendum to “Coefficients of half-integral weight modular forms”: [J. Number Theory 99 (2003) 164–179] (2004) (5)
- A note on a question of J. Nekovár and the Birch and Swinnerton-Dyer Conjecture (1998) (5)
- Even Values of Ramanujan’s Tau-Function (2021) (4)
- The Residue of p(N) Modulo Small Primes (1998) (4)
- Divisibility criteria for class numbers of imaginary quadratic fields (2006) (4)
- Quadratic twists of elliptic curves and class numbers (2020) (4)
- Partition-theoretic formulas for arithmetic densities, II (2020) (4)
- $p$-adic properties of modular shifted convolution Dirichlet series (2014) (4)
- My Search for Ramanujan: How I Learned to Count (2016) (4)
- Gauss's $_2F_1$ hypergeometric function and the congruent number elliptic curve (2010) (4)
- Differential Endomorphisms for Modular Forms On Γ0(4) (2001) (4)
- GAUSS’S 2F1 HYPERGEOMETRIC FUNCTION AND THE CONGRUENT NUMBER ELLIPTIC CURVE (2010) (4)
- Recent Work on the Partition Function (2013) (3)
- Parity of Fourier coefficients of modular forms (1997) (3)
- p-Adic Properties of Values of the Modular j-Function (2004) (3)
- Identities for traces of singular moduli (2005) (3)
- Partitions and McKay numbers for Sn (2004) (3)
- Zeros in the character tables of symmetric groups with an $\ell $ -core index (2022) (3)
- A Note On Non-ordinary Primes (2015) (3)
- IDENTITIES FOR TRACES OF SINGULAR MODULI (2005) (3)
- Ramanujan, Taxicabs, Birthdates, ZIP Codes, and Twists (1997) (3)
- Distribution of values of Gaussian hypergeometric functions (2021) (3)
- Corrigendum to “On divisors of modular forms” [Adv. Math. 329 (2018) 541–554] (2020) (3)
- THE PARTITION FUNCTION AND HECKE OPERATORS (2011) (3)
- 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)
- The Life and Work of R.A. Rankin (1915–2001) (2003) (2)
- Probabilities as Values of Modular Forms and Continued Fractions (2009) (2)
- Duality involving the mock theta function f(q) (2008) (2)
- ALGEBRAICITY OF HARMONIC MAASS FORMS (2009) (2)
- HECKE OPERATORS AND THE q-EXPANSION OF MODULAR FORMS (2003) (2)
- My Search for Ramanujan (2016) (2)
- On “good” half-integral weight modular forms (2000) (2)
- HECKE OPERATORS AND THE q-EXPANSION OF MODULAR FORMS (2004) (2)
- HECKE OPERATORS AND THE q-EXPANSION OF MODULAR FORMS (2004) (2)
- The 1729 K3 surface (2015) (2)
- Weighted Generating Functions and Configuration Results for Type II Lattices and Codes (2009) (2)
- QUADRATIC TWISTS OF MODULAR FORMS AND ELLIPTIC CURVES (2004) (2)
- Distributions of Hook lengths in integer partitions (2022) (2)
- Moonshine for M 24 and Donaldson invariants of C P 2 (2013) (2)
- Arithmetic of the Partition Function (2001) (2)
- MODULAR FORMS ARISING FROM Q(n) AND DYSON’S RANK (2009) (2)
- Congruences for $\sb 3F\sb 2$ hypergeometric functions over finite fields (2002) (2)
- Singular moduli generating functions for modular curves and surfaces (2006) (2)
- Algebraicity of harmonic Maass forms (2009) (1)
- The Eichler Integral of E 2 and q-brackets of t-hook Functions (2020) (1)
- Multiquadratic fields generated by characters of A (2019) (1)
- The partition function and Hecke operators (2011) (1)
- Remembering Basil Gordon , 1931 – 2012 (2013) (1)
- The 1729 K3 surface (2016) (1)
- My Parents’ Generation (2016) (1)
- 2-ADIC PROPERTIES OF CERTAIN MODULAR FORMS (2004) (1)
- The partition function modulo 4 (2022) (1)
- Partitions into Distinct Parts and Elliptic Curves (1998) (1)
- Topics in Number Theory (1999) (1)
- Limiting Betti distributions of Hilbert schemes on n points (2021) (1)
- MOCK THETA FUNCTION CONJECTURE AND PARTITION RANKS (2005) (1)
- AGM and Jellyfish Swarms of Elliptic Curves (2021) (1)
- Number theoretic generalization of the monster denominator formula (2017) (1)
- Singular moduli generating functions for modular curves and surfaces (2007) (1)
- Moonshine (2015) (1)
- TheLastWordsof aGenius (2010) (0)
- Erratum to: The 1729 K3 surface (2017) (0)
- Weierstrass points on modular curves (2003) (0)
- Triumph over Racism (2016) (0)
- On the work of Basil Gordon (2006) (0)
- Black holes and class groups (2018) (0)
- HITTING MY STRIDE (2016) (0)
- Counting matrix points on certain varieties over finite fields (2023) (0)
- These Formulas Defeated Me Completely (2016) (0)
- HOOK LENGTHS AND 3-CORES (2008) (0)
- I Believe in Santa (2016) (0)
- Integer weight modular forms (2003) (0)
- I Beg to Introduce Myself (2016) (0)
- Topics in Number Theory: In Honor of B. Gordon and S. Chowla (2011) (0)
- Some Eichler-Selberg Trace Formulas (2023) (0)
- Central values of modular -functions and applications (2003) (0)
- Permission from the Goddess (2016) (0)
- Rank zero quadratic twists of modular elliptic curves (2018) (0)
- Class numbers of quadratic fields (2003) (0)
- VALUES OF GAUSSIAN HYPERGEOMETRIC SERIES (1997) (0)
- Traces of singular moduli and class equations (2003) (0)
- Honoring a Gift from Kumbakonam, Volume 53, Number 6 (2006) (0)
- Integers represented by ternary quadratic forms (1999) (0)
- The Pirate Professor (2016) (0)
- Preface (2014) (0)
- Tamagawa products of elliptic curves over $\mathbb{Q}$ (2021) (0)
- EULER–KRONECKER CONSTANTS FOR CYCLOTOMIC FIELDS (2022) (0)
- Cool theorems in number theory proved by undergrads (2012) (0)
- The Idea of Ramanujan (2016) (0)
- Fourier coefflcients of half-integral weight modular forms modulo t (2016) (0)
- The legacy of Ramanujan's mock theta functions: Harmonic Maass forms in number theory (2012) (0)
- Maximal Multiplicative Properties of Partitions (2015) (0)
- Modular forms arising from Q(n) and Dyson's rank (2011) (0)
- Eichler–Shimura theory for mock modular forms (2012) (0)
- Ip2 on Sidorenko's Conjecture Ip3 Forcing Large Transitive Subtournamets Ip5 Coloring 3-colorable Graphs; Graph Theory Fi- Nally Strikes Back! (0)
- Fields generated by characters of finite linear groups (2019) (0)
- Modular forms are everywhere: celebration of Don Zagier’s 65th birthday (2019) (0)
- The Tragic End (2016) (0)
- Basic hypergeometric generating functions for -values (2003) (0)
- Proof of the umbral moonshine conjecture (2015) (0)
- Number theory and modular forms : papers in memory of Robert A. Rankin (2003) (0)
- Half-integral weight modular forms (2003) (0)
- My Childhood (1970–1984) (2016) (0)
- I Count Now (2016) (0)
- R T ] 2 6 N ov 2 01 5 Proof of the Umbral Moonshine Conjecture (2018) (0)
- Proof of the elliptic expansion Moonshine Conjecture of C\u{a}ld\u{a}raru, He, and Huang (2021) (0)
- Pariah moonshine (2017) (0)
- Gaussian hypergeometric functions (2003) (0)
- Product expansions of modular forms on ₂(ℤ) (2003) (0)
- Higher width moonshine (2018) (0)
- Heights of points on elliptic curves over $\mathbb {Q}$ (2020) (0)
- Singular moduli generating functions for modular curves and surfaces (2007) (0)
- Srinivasa Ramanujan: in celebration of the centenary of his election as FRS (2019) (0)
- Weierstrass mock modular forms and elliptic curves (2015) (0)
- The arithmetic of the coefficients of half-integral weight Eisenstein series (2003) (0)
- Hasse invariants for the Clausen elliptic curves (2012) (0)
- Together at Last (2016) (0)
- Modular forms are everywhere: celebration of Don Zagier’s 65th birthday (2019) (0)
- Note added in proof (1984) (0)
- Number Theory and Modular Forms (2003) (0)
- Hypergeometry and the AGM over Finite Fields (2023) (0)
- Donaldson invariants of C P 2 and mock theta functions (2012) (0)
- An Unexpected Letter (2016) (0)
- Contemporary Mathematics Ramanujan ’ s radial limits (2013) (0)
- Donaldson invariants of C P 2 and mock theta functions (2012) (0)
- Singular moduli generating functions for modular curves and surfaces (2007) (0)

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## Other Resources About Ken Ono

## What Schools Are Affiliated With Ken Ono?

Ken Ono is affiliated with the following schools: