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**About this book :- **
**Modular Functions and Dirichlet Series in Number Theory ** written by
** Tom M. Apostol **.

This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years.

The second volume presupposes a 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 the present volume is devoted to elliptic functions and modular functions with some of their number-theoretic applications. Among the major topics treated are Rademacher's convergent series for the partition function, Lehner's congruences for the Fourier coefficients of the modular functionj( r), and Hecke's theory of entire forms with multiplicative Fourier coefficients. The last gives an account of Bohr's theory of equivalence of general Dirichlet series.

Both volumes of this work emphasize classical aspects of a subject wh ich in recent years has undergone a great deal of modern development. It is hoped that these volumes will help the nonspecialist become acquainted with an important and fascinating part of mathematics and, at the same time, will provide some of the background that belongs to the repertory of every specialist in the field.

(Tom M. Apostol)

**Book Detail :- **
** Title: ** Modular Functions and Dirichlet Series in Number Theory
** Edition: **
** Author(s): ** Tom M. Apostol
** Publisher: ** Springer New York
** Series: ** Graduate Texts in Mathematics
** Year: ** 1976
** Pages: ** 206
** Type: ** PDF
** Language: ** English
** ISBN: ** 978-1-4684-9912-4,978-1-4684-9910-0
** Country: ** US
**Download Similar Books from Amazon **

**About Author :- **
The author ** Tom M. Apostol ** joined the Caltech faculty in 1950 and is Professor of Mathematics, Emeritus. He is internationally known for his books on Calculus, Analysis, and Analytic Number Theory, (translated into 7 languages), and for creating Project MATHEMATICS!, a video series that brings mathematics to life with computer animation, live action, music, and special effects. The videos have won first-place honors at a dozen international festivals, and were translated into Hebrew, Portuguese, French, and Spanish. Apostol has published 102 research papers, has written two chapters for the Digital Library of Mathematical Functions (2010), and is coauthor of three texts for the physics telecourse.

He has received several awards for research and teaching. In 1978 he was a visiting professor at the University of Patras, Greece, and in 2001 was elected a Corresponding Member of the Academy of Athens, where he delivered his inaugural lecture in Greek. In 2012 he was selected to be a Fellow of the American Mathematical Society.

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.

** • Download PDF Mathematical Analysis, 2E, Tom M. Apostol **

** • Download PDF Mathematical Analysis, 2E, Solution Manual, Tom M. Apostol **

** • Download PDF Introduction to Analytic Number Theory (2E) by Tom M. Apostol **

** • Download PDF Introduction to Analytic Number Theory (Solutions Manual) by Tom M. Apostol **

** • Download PDF Introduction to Analytic Number Theory by Tom M. Apostol **

** • Download PDF Modular Functions and Dirichlet Series in Number Theory, Tom M. Apostol **

** • Download PDF New Horizons in Geometry, Tom M. Apostol, Mamikon A Mnatsakanian **

** • Download PDF Selected Papers on Precalculus, Tom M. Apostol **

** • Download PDF Calculus I: One-Variable Calculus, with an Introduction to Linear Algebra, 2E, Tom M. Apostol **

** • Download PDF Calculus II: Multi-Variable Calculus & Linear Algebra, with Applications to Diff. Equations & Probability, Tom M. Apostol **

** • Download PDF Multimedia Tools for Communicating Mathematics by Tom M. Apostol, Jonathan Borwein, Maria H. Morales, José F. Rodrigues, Konrad Polthier **

** • Download PDF The Mechanical Universe: Mechanics and Heat by Steven C. Frautschi, Richard P. Olenick, Tom M. Apostol, David L. Goodstein **

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**Book Contents :- **
**Modular Functions and Dirichlet Series in Number Theory ** written by
** Tom M. Apostol **
cover the following topics.
'

1. Elliptic functions

2. The Modular group and modularfunctions

3. The Dedekind eta function

4. Congruences Jor the coeJJicients oJ the modular function j

5. Rademacher's series Jor the partition function

6. Modular forms with multiplicative coefficients

7. Kronecker's theorem with applications

8. General Dirichlet series and Bohr' s equivalence theorem

Bibliography

Index of special symbols

Index

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