Modular Functions and Dirichlet Series in Number Theory: Vol 41 (Graduate Texts in Mathematics) - Hardcover

Apostol, Tom M.

9783540971276: Modular Functions and Dirichlet Series in Number Theory: Vol 41 (Graduate Texts in Mathematics)

Hardcover

ISBN 10: 3540971270 ISBN 13: 9783540971276

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1989

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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 three.

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Review

From the reviews of the second edition:

“Apostol is an excellent writer of mathematics and the topics that are covered in this book are covered thoroughly in a concise, precise manner. … the writing is characterized by its easy, readable, fluid style. Each chapter is complemented with a nice set of exercises.” (�lvaro Lozano-Robledo, The Mathematical Association of America, June, 2011)

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