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

Apostol, Tom M.

Hardcover

ISBN 10: 0387971270 ISBN 13: 9780387971278

Verlag: Springer, 1989

Inhaltsangabe

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 com­ parable 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 chapter gives an account of Bohr's theory of equivalence of general Dirichlet series. Both volumes of this work emphasize classical aspects of a subject which 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. This volume, like the first, is dedicated to the students who have taken this course and have gone on to make notable contributions to number theory and other parts of mathematics. T.M.A. January, 1976 * The first volume is in the Springer-Verlag series Undergraduate Texts in Mathematics under the title Introduction to Analytic Number Theory.

Über diesen Titel

Über die Autorin bzw. den Autor

Tom A. Apostol, Emeritus Professor at the California Institute of Technology, is the author of several highly regarded texts on calculus, analysis, and number theory, and is Director of Project MATHEMATICS!, a series of computer-animated mathematics videotapes.

Von der hinteren Coverseite

This volume is a sequel to INTRODUCTION TO ANALYTIC NUMBER THEORY (UTM). Most of the book is concerned with a classical treatment of elliptic and modular functions with applications to number theory. This includes the asymptotic theory of partitions and multiplicative properties of coefficients of modular forms. The book presupposes a knowledge of elementary number theory and the rudiments of real and complex analysis.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 1989
• Sprache: Englisch
• ISBN 10: 0387971270
• ISBN 13: 9780387971278
• Einband: Gebundene Ausgabe
• Auflage: 2
• Anzahl der Seiten: 217
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland