Elementary Dirichlet Series and Modular Forms Hard cover - 2007 - 2007th Edition
by Goro Shimura
- New
- Hardcover
Description
Standard delivery: 7 to 12 days
Details
- Title Elementary Dirichlet Series and Modular Forms
- Author Goro Shimura
- Binding Hard Cover
- Edition number 2007th
- Edition 2007
- Condition New
- Pages 152
- Volumes 1
- Language ENG
- Publisher Springer
- Date 2007-09-10
- Illustrated Yes
- Features Bibliography, Illustrated, Index, Table of Contents
- Bookseller's Inventory # ria9780387724737_pod
- ISBN 9780387724737 / 0387724737
- Weight 0.72 lbs (0.33 kg)
- Dimensions 9.34 x 6.48 x 0.51 in (23.72 x 16.46 x 1.30 cm)
- Library of Congress subjects Forms, Modular, L-functions
- Library of Congress Catalog Number 2007931368
- Dewey Decimal Code 515.243
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From the publisher
From the rear cover
The main topics of the book are the critical values of Dirichlet L-functions and Hecke L-functions of an imaginary quadratic field, and various problems on elliptic modular forms. As to the values of Dirichlet L-functions, all previous papers and books reiterate a single old result with a single old method. After a review of elementary Fourier analysis, the author presents completely new results with new methods, though old results will also be proved. No advanced knowledge of number theory is required up to this point. As applications, new formulas for the second factor of the class number of a cyclotomic field will be given.
The second half of the book assumes familiarity with basic knowledge of modular forms. However, all definitions and facts are clearly stated, and precise references are given. The notion of nearly holomorphic modular forms is introduced and applied to the determination of the critical values of Hecke L-functions of an imaginary quadratic field. Other notable features of the book are: (1) some new results on classical Eisenstein series; (2) the discussion of isomorphism classes of elliptic curves with complex multiplication in connection with their zeta function and periods; (3) a new class of holomorphic differential operators that send modular forms to those of a different weight.
The book will be of interest to graduate students and researchers who are interested in special values of L-functions, class number formulae, arithmetic properties of modular forms (especially their values), and the arithmetic properties of Dirichlet series. It treats in detail, from an elementary viewpoint, the simplest cases of a fundamental area of ongoing research, the only prerequisite being a basic course in algebraic number theory.
