The web of modularity: arithmetic of the coefficients of modular forms and \(q\)-series. (English) Zbl 1119.11026

Ono, Ken

CBMS Regional Conference Series in Mathematics 102. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3368-5/pbk). viii, 216 p. (2004).

This monograph is an expanded version of the ten lectures the author presented at the NSF-CBMS Regional Conference at the University of Illinois at Urbana-Champaign. He considers recent work on partitions, basic hypergeometric functions, Gaussian hypergeometric functions, super-congruences, Weierstrass points on modular curves, singular moduli, class numbers, \(L\)-values, and elliptic curves. At the end of most chapters he lists some open problems and questions.

Reviewer: Florin Nicolae (Berlin)

MSC:

11F30	Fourier coefficients of automorphic forms
11-02	Research exposition (monographs, survey articles) pertaining to number theory
33-02	Research exposition (monographs, survey articles) pertaining to special functions
05A30	\(q\)-calculus and related topics
11F11	Holomorphic modular forms of integral weight
11F37	Forms of half-integer weight; nonholomorphic modular forms
33Cxx	Hypergeometric functions
33Dxx	Basic hypergeometric functions

Keywords:

Fourier coefficients of modular forms