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The web of modularity: arithmetic of the coefficients of modular forms and $q$-series. (English) Zbl 1119.11026
CBMS Regional Conference Series in Mathematics 102. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3368-5/pbk). viii, 216 p. $ 45.00 (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.

MSC:
11F30Fourier coefficients of automorphic forms
11-02Research monographs (number theory)
33-02Research monographs (special functions)
05A30$q$-calculus and related topics
11F11Holomorphic modular forms of integral weight
11F37Forms of half-integer weight, etc.
33CxxHypergeometric functions
33DxxBasic hypergeometric functions