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Elementary Dirichlet Series and Modular Forms / Edition 1

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Overview

A book on any mathematical subject beyond the textbook level is of little value unless it contains new ideas and new perspectives. It helps to include new results, provided that they give the reader new insights and are presented along with known old results in a clear exposition. It is with this philosophy that the author writes this volume. The two subjects, Dirichlet series and modular forms, are traditional subjects, but here they are treated in both orthodox and unorthodox ways. Regardless of the unorthodox treatment, the author has made the book accessible to those who are not familiar with such topics by including plenty of expository material.

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Editorial Reviews

From the Publisher

From the reviews:

"This book contains new results, e.g., new formulas for special values of certain Dirichlet series. … Shimura’s exposition, shaped to his (celebrated and) distinctive viewpoint, serves as the ideal platform for the new material. … by dint of the prestige of the author and the subject, it undoubtedly deserves a place in a college library. … Summing Up: Recommended. Upper-division undergraduates through faculty." (D. V. Feldman, CHOICE, Vol. 45 (9), 2008)

"It will be of great interest for everybody who is interested in modular forms and/or L-series. … the monograph will be accessible to graduate students and will quickly lead them to frontiers of current research. The book is written in the well-known masterly style of the author … ." (Jürgen Elstrodt, Zentralblatt MATH, Vol. 1148, 2008)

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Product Details

  • ISBN-13: 9781441924780
  • Publisher: Springer New York
  • Publication date: 11/19/2010
  • Series: Springer Monographs in Mathematics Series
  • Edition description: Softcover reprint of hardcover 1st ed. 2007
  • Edition number: 1
  • Pages: 152
  • Product dimensions: 5.90 (w) x 9.00 (h) x 0.40 (d)

Table of Contents

Preliminaries on Modular Forms and Dirichlet Series.- Critical Values of Dirichlet L-functions.- The Case of Imaginary Quadratic Fields and Nearly Holomorphic Modular Forms.- Eisenstein Series.- Critical Values of Dirichlet Series Associated with Imaginary Quadratic Fields.- Supplementary Results.

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