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The web of modularity : arithmetic of the coefficients of modular forms and q-series

- K. Ono
- Mathematics
- 22 December 2003

Basic facts Integer weight modular forms Half-integral weight modular forms Product expansions of modular forms on $\mathrm{SL}_2(\mathbb{Z})$ Partitions Weierstrass points on modular curves Traces… Expand

A Gaussian hypergeometric series evaluation and Apéry number congruences

- S. Ahlgren, K. Ono
- Mathematics
- 5 January 2000

If p is prime, then let φp denote the Legendre symbol modulo p and let p be the trivial character modulo p. As usual, let n+1Fn(x)p := n+1Fn „ φp, φp, . . . , φp p, . . . , p | x « p be the Gaussian… Expand

THE f(q) MOCK THETA FUNCTION CONJECTURE AND PARTITION RANKS

- K. Ono
- Mathematics
- 2005

In 1944, Freeman Dyson initiated the study of ranks of integer partitions. Here we solve the classical problem of obtaining formulas for Ne(n) (resp. No(n)), the number of partitions of n with even… Expand

Defect zero p-blocks for finite simple groups

- A. Granville, K. Ono
- Mathematics
- 1 December 1996

We classify those finite simple groups whose Brauer graph (or decomposition matrix) has a p-block with defect 0, completing an investigation of many authors. The only finite simple groups whose… Expand

Dyson’s ranks and Maass forms

- K. Bringmann, K. Ono
- Mathematics
- 17 March 2010

which were defined by Ramanujan and Watson decades ago. In his last letter to Hardy dated January 1920 (see pages 127-131 of [27]), Ramanujan lists 17 such functions, and he gives 2 more in his “Lost… Expand

Values of Gaussian hypergeometric series

- K. Ono
- Mathematics
- 1998

Let p be prime and let GF (p) be the finite field with p elements. In this note we investigate the arithmetic properties of the Gaussian hypergeometric functions 2F1(x) =2 F1 ( φ, φ | x ) and 3F2(x)… Expand

Congruence properties for the partition function

- S. Ahlgren, K. Ono
- MathematicsProceedings of the National Academy of Sciences…
- 23 October 2001

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Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms

- J. Bruinier, K. Ono
- Mathematics
- 6 April 2011

Unearthing the visions of a master: harmonic Maass forms and number theory

- K. Ono
- Mathematics
- 2008

Together with his collaborators, most notably Kathrin Bringmann and Jan Bruinier, the author has been researching harmonic Maass forms. These non-holomorphic modular forms play central roles in many… Expand

Jensen polynomials for the Riemann zeta function and other sequences

- Michael J. Griffin, K. Ono, Larry Rolen, D. Zagier
- MathematicsProceedings of the National Academy of Sciences
- 19 February 2019

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