The web of modularity : arithmetic of the coefficients of modular forms and q-series
By Ken Ichi Ono. 2003
968 citations recorded by the source corpus.
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/17d416c4cf8c4eb29ca760f39585dd7d3ceb5a5c
How researchers see this paper
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In Algebra and Number Theory
- Ken Ichi Ono
- Kathrin Bringmann
- Zhi-Wei Sun
- Robert C. Rhoades
- Dermot McCarthy
- William Duke
- Amanda Folsom
- Robert Osburn
In Applied Mathematics
- Zhi-Wei Sun
- Cristian-Silviu Radu
- Kathrin Bringmann
- William Duke
- Stephanie Treneer
- Robert Osburn
- Amanda Folsom
- Jan H. Bruinier
Citations in the corpus
- ℓ-Adic properties of the partition function☆☆☆ (2012, background): “65 of [28]), it follows that A`(z) is a weight (`− 1)/2 holomorphic modular form on Γ0(`) with Nebentypus (• ` ) .”
- Super congruences and Euler numbers (2010, background): “Ono’s book [O] and the papers [AO], [K], [MO], [M03b], [M05], [M08], [Mc] and [OS] for such advanced approach to super congruences.”
- Gaussian hypergeometric functions and traces of Hecke operators (2004, background): “…∈ { −1, 4, 1 4 ,−8,−1 8 , 64, 1 64 } , then, for all but finitely many primes p, it turns out that 3F2(λ)p is essentially the p-th Fourier coefficient of an explicit weight 3 newform with complex multiplication that is associated to a certain singular K3 surface Xλ (see Corollary 11.20 of [18]).”
- Unearthing the visions of a master: harmonic Maass forms and number theory (2008, background): “For the remainder of the paper, we shall assume that the reader is familiar with the classical theory of elliptic modular forms (for example, see [71] [84] [125] [134] [143] [155] [164] [177] [185] [193] [196]).”
- Congruences for the coefficients of weakly holomorphic modular forms (2006, background): “For a more detailed treatment, see for example [18], [8] or [14].”
- A proof of Subbarao's conjecture (2011, background): “For more results of this type see Ken Ono’s book [16].”