Modular Functions and Dirichlet Series in Number Theory

ISBN-10: 0387971270
ISBN-13: 9780387971278
Edition: 2nd 1990 (Revised)
Authors: Tom M. Apostol
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Description: This volume is a sequel to the author's Introduction to Analytic Number Theory (UTM 1976, 3rd Printing 1986). It presupposes an undergraduate background in number theory comparable to that provided in the first volume, together with a knowledge of  More...

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Book details

List price: $79.95
Edition: 2nd
Copyright year: 1990
Publisher: Springer
Publication date: 5/22/1997
Binding: Hardcover
Pages: 207
Size: 6.00" wide x 9.00" long x 0.50" tall
Weight: 1.276
Language: English

This volume is a sequel to the author's Introduction to Analytic Number Theory (UTM 1976, 3rd Printing 1986). It presupposes an undergraduate background in number theory comparable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of this book is devoted to a classical treatment of elliptic and modular functions with some of their number-theoretic applications. Among the major topics covered are Rademacher's convergent series for the partition modular function, Lehner's congruences for the Fourier coefficients of the modular function j, and Hecke's theory of entire forms with multiplicative Fourier coefficients. The last chapter gives an account of Bohr's theory of equivalence of general Dirichlet series. In addition to the correction of misprints, minor changes in the exercises and an updated bibliography, this new edition includes an alternative treatment of the transformation formula for the Dedekind eta function, which appears as a five-page supplement to Chapter 3.

Tom Apostol is an Emeritus Professor of Mathematics at the California Institute of Technology.

Elliptic functions
The Modular group and modular functions
The Dedekind eta function
Congruences for the coefficients of the modular function j.
Rademacher's series for the partition function
Modular forms with multiplicative coefficients
Kronecker's theorem with applications
General Dirichlet series and Bohr's equivalence theorem

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