Modular

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Springer-Verlag, 1990 - Mathematics - 204 pages
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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 3.

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About the author (1990)

Tom M. Apostol joined the California Institute of Technology faculty in 1950 and is now Professor of Mathematics, Emeritus. He is internationally known for his textbooks on Calculus, Analysis, and Analytic Number Theory, which have been translated into 5 languages, and for creating Project MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects. The videos have won first-place honors at a dozen international video festivals, and have been translated into Hebrew, Portuguese, French, and Spanish. His list of publications includes 98 research papers, 46 of them published since he retired in 1992. He has received several awards for his research and teaching. In 1978 he was a visiting professor at the University of Patras in Greece, and in 2000 was elected a Corresponding Member of the Academy of Athens, where he delivered his inaugural lecture in Greek.

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