Description

Book Synopsis
Modular forms appear in many ways in number theory. This book details various roles that modular forms and $q$-series play in number theory, such as applications and connections to basic hypergeometric functions, Gaussian hypergeometric functions, super-congruences, Weierstrass points on modular curves, singular moduli, and class numbers.

Table of Contents
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 of singular moduli and class equations Class numbers of quadratic fields Central values of modular $L$-functions and applications Basic hypergeometric generating functions for $L$-values Gaussian hypergeometric functions Bibliography Index.

The Web of Modularity

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    A Paperback by American Mathem American Mathem

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      Book details

      Publisher American Mathematical Society
      Published 12/30/2003 12:00:00 AM
      ISBN-13 9780821833681
      978-0821833681
      ISBN-10 0821833685

      Description

      Book Synopsis
      Modular forms appear in many ways in number theory. This book details various roles that modular forms and $q$-series play in number theory, such as applications and connections to basic hypergeometric functions, Gaussian hypergeometric functions, super-congruences, Weierstrass points on modular curves, singular moduli, and class numbers.

      Table of Contents
      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 of singular moduli and class equations Class numbers of quadratic fields Central values of modular $L$-functions and applications Basic hypergeometric generating functions for $L$-values Gaussian hypergeometric functions Bibliography Index.

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