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American Mathematical Society Modular Forms: A Classical Approach (Graduate Studies in Mathematics)

Name: Modular Forms: A Classical Approach (Graduate Studies in Mathematics)
Brand: American Mathematical Society
Price: 87.95 GBP
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Algebra

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Description

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 Atkin-Lehner-Li theory of newforms and including the theory of Eisenstein series, Rankin-Selberg 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 half-integral 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 little-known 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 self-contained; the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on are given in a separate chapter.

Key Features

Modular Forms: A Classical Approach (Graduate Studies in Mathematics, 179, Volume 179)

Product type: ABIS BOOK

Brand: American Mathematical Society

Product Specifications

Brand: American Mathematical Society
Format: hardcover
ASIN: 0821849476
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 30 July 2017
Listed Since: 18 April 2017

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American Mathematical Society Modular Forms: A Classical Approach (Graduate Studies in Mathematics)

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