Modular forms : a classical approach
 Responsibility
 Henri Cohen, Fredrik Strömberg.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2017]
 Copyright notice
 ©2017
 Physical description
 xii, 700 pages : illustrations ; 26 cm.
 Series
 Graduate studies in mathematics ; v. 179.
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA243 .C64 2017  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Cohen, Henri, author.
 Contributor
 Strömberg, Fredrik, 1973 author.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 679691) and indexes.
 Contents

 IntroductionElliptic functions, elliptic curves, and theta functionBasic toolsThe modular groupGeneral aspects of holomorphic and nonholomorphic modular formsSets of $2 \times 2$ integer matricesModular forms and functions on subgroupsEisenstein and Poincare seriesFourier coefficients of modular formsHecke operators and Euler productsDirichlet series, functional equations, and periodsUnfolding and kernelsAtkinLehnerLi theoryTheta functionsMore general modular forms: An introductionBibliographyIndex of notationGeneral index.
 (source: Nielsen Book Data)
 Publisher's Summary
 ["The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and ``fun'' subject in itself and abounds with an amazing number of surprising identities.This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the AtkinLehnerLi theory of newforms and including the theory of Eisenstein series, RankinSelberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as halfintegral weight, Hilbert, Jacobi, Maass, and Siegel modular forms.Some ``gems'' of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's littleknown theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms.This book is essentially selfcontained; the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on are given in a separate chapter.", {"source"=>"(source: Nielsen Book Data)"}, "9780821849477", "20171106"]
Subjects
Bibliographic information
 Publication date
 2017
 Copyright date
 2017
 Series
 Graduate studies in mathematics ; 179
 ISBN
 9780821849477 hardcover alkaline paper
 0821849476 hardcover alkaline paper