Modular functions and Dirichlet series in number theory
 Responsibility
 Tom M. Apostol.
 Language
 English.
 Edition
 2nd ed.
 Imprint
 New York : SpringerVerlag, c1990.
 Physical description
 x, 204 p. : ill. ; 24 cm.
 Series
 Graduate texts in mathematics ; 41.
Access
Creators/Contributors
 Author/Creator
 Apostol, Tom M.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 196198).
 Contents

 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. Supplement. Bibliography. Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 numbertheoretic 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 fivepage supplement to chapter three.
(source: Nielsen Book Data)  Supplemental links

Publisher description
Table of contents only
Subjects
 Subject
 Number theory.
 Elliptic functions.
 Modular functions.
 Dirichlet series.
 Nombres, théorie des.
 Fonctions elliptiques.
 Fonctions modulaires.
 Dirichlet, séries de.
 Fonctions elliptiques.
 Fonctions modulaires.
 Dirichlet, Séries de.
 Funções e formas modulares.
 Séries de dirichlet.
 Teoria dos números.
 DirichletReihe.
 Modulfunktion.
 Zahlentheorie.
 Dirichlet series
 Elliptic functions
 Modular functions
 Number theory
Bibliographic information
 Publication date
 1990
 Series
 Graduate texts in mathematics ; 41
 ISBN
 0387971270 (alk. paper)
 9780387971278 (alk. paper)
 3540971270
 9783540971276