Modular Functions and Dirichlet Series in Number Theory / Edition 2

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A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.

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Editorial Reviews

From the Publisher
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.” (Álvaro Lozano-Robledo, The Mathematical Association of America, June, 2011)

A clean, elegant, absolutely lovely text derived from a course which the author has taught for many years at Caltech, conceived as a companion to his Introduction to analytic number theory, and differing from its first edition (1976) mainly by the addition of a few pages of new material. Provides graduate students, advanced undergraduates and general mathematical readers with a splendid introduction to some classical material of unsurpassed beauty, and to a field of remarkable richness which remains even today quite lively. Eight chapters, with exercises and essential references. (NW) Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780387971278
  • Publisher: Springer New York
  • Publication date: 12/1/1989
  • Series: Graduate Texts in Mathematics Series, #41
  • Edition description: 2nd ed. 1990. Corr. 2nd printing 1997
  • Edition number: 2
  • Pages: 207
  • Product dimensions: 6.20 (w) x 9.20 (h) x 1.00 (d)

Table of Contents

1: Elliptic functions. 2: The Modular group and modular functions. 3: The Dedekind eta function. 4: Congruences for the coefficients of the modular function j. 5: Rademacher's series for the partition function. 6: Modular forms with multiplicative coefficients. 7: Kronecker's theorem with applications. 8: General Dirichlet series and Bohr's equivalence theorem.

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