This section provides an overview of the "Graduate Texts in Mathematics" series, published by Springer Science+Business Media, LLC. The series includes a wide range of advanced mathematical texts, covering topics such as set theory, complex analysis, functional analysis, algebra, topology, and number theory. Each volume is authored by renowned mathematicians and is designed to serve as a comprehensive resource for graduate students and researchers in mathematics.
The specific volume highlighted is "Modular Functions and Dirichlet Series in Number Theory" by Tom M. Apostol, published in its second edition. This book is part of a two-volume series that evolved from a course at the California Institute of Technology. The second volume focuses on elliptic and modular functions, their number-theoretic applications, and related topics such as Rademacher's series for the partition function, Lehner's congruences, and Hecke's theory of entire forms. The book also includes a chapter on Bohr's theory of equivalence of Dirichlet series.
The preface to the second edition notes that the major change is an alternate treatment of the transformation formula for the Dedekind eta function, with minor updates and corrections throughout the text. The book is dedicated to students who have contributed significantly to number theory and other areas of mathematics.This section provides an overview of the "Graduate Texts in Mathematics" series, published by Springer Science+Business Media, LLC. The series includes a wide range of advanced mathematical texts, covering topics such as set theory, complex analysis, functional analysis, algebra, topology, and number theory. Each volume is authored by renowned mathematicians and is designed to serve as a comprehensive resource for graduate students and researchers in mathematics.
The specific volume highlighted is "Modular Functions and Dirichlet Series in Number Theory" by Tom M. Apostol, published in its second edition. This book is part of a two-volume series that evolved from a course at the California Institute of Technology. The second volume focuses on elliptic and modular functions, their number-theoretic applications, and related topics such as Rademacher's series for the partition function, Lehner's congruences, and Hecke's theory of entire forms. The book also includes a chapter on Bohr's theory of equivalence of Dirichlet series.
The preface to the second edition notes that the major change is an alternate treatment of the transformation formula for the Dedekind eta function, with minor updates and corrections throughout the text. The book is dedicated to students who have contributed significantly to number theory and other areas of mathematics.