Elementary Dirichlet Series and Modular Forms

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Last edited by MARC Bot
July 5, 2025 | History

Elementary Dirichlet Series and Modular Forms

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.

Publish Date
Publisher
Springer
Language
English
Pages
152

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Edition Availability
Cover of: Elementary Dirichlet Series and Modular Forms
Elementary Dirichlet Series and Modular Forms
2008, Springer London, Limited
in English
Cover of: Elementary Dirichlet Series and Modular Forms
Elementary Dirichlet Series and Modular Forms
September 24, 2007, Springer
in English

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Book Details


Edition Notes

Springer Monographs in Mathematics

Classifications

Library of Congress
QA241-247.5QA564-609, QA295 .S545 2007, QA295 .S55 2007

Edition Identifiers

Open Library
OL7447883M
ISBN 10
0387724737
ISBN 13
9780387724737
LCCN
2007931368
OCLC/WorldCat
154711930
LibraryThing
5544842
Goodreads
3141255

Work Identifiers

Work ID
OL8058010W

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Download catalog record: RDF / JSON / OPDS | Wikipedia citation
July 5, 2025 Edited by MARC Bot import existing book
March 28, 2025 Edited by ImportBot Redacting ocaids
May 28, 2023 Edited by MARC Bot import existing book
December 29, 2022 Edited by MARC Bot import existing book
April 29, 2008 Created by an anonymous user Imported from amazon.com record