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Modular forms : a classical and computational introduction /

This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to such diverse subjects as the theory of quadrati...

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Bibliographic Details
Main Authors: Kilford, L. J. P. Lloyd James Peter
Corporate Authors: World Scientific Firm
Published: Imperial College Press ; Distributed by World Scientific Publishing Co.,
Publisher Address: London : Singapore :
Publication Dates: 2008.
Literature type: eBook
Language: English
Subjects:
Forms, Modular > Data processing
Algebraic spaces > Data processing
Electronic books
Online Access: http://www.worldscientific.com/worldscibooks/10.1142/P564#t=toc
Summary: This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to such diverse subjects as the theory of quadratic forms, the proof of Fermat's last theorem and the approximation of pi. It provides a balanced overview of both the theoretical and computational sides of the subject, allowing a variety of courses to be taught from it.
Item Description: "This book is based on notes for lectures given at the Mathematical Institute at the University of Oxford ... 2004-2007"--Introd.
Carrier Form: 1 online resource (xii,224pages) : illustrations
Bibliography: Includes bibliographical references (pages 205-216) and index.
ISBN: 9781848162143 (electronic bk.)
CLC: O156
Contents: 1. Historical overview. 1.1. 18th century - a prologue. 1.2. 19th century - the classical period. 1.3. Early 20th century - arithmetic applications. 1.4. Later 20th century - the link to elliptic curves. 1.5. The 21st century - the Langlands program -- 2. Introduction to modular forms. 2.1. Modular forms for [symbol]. 2.2. Eisenstein series for the full modular group. 2.3. Computing Fourier expansions of Eisenstein series. 2.4. Congruence subgroups. 2.5. Fundamental domains. 2.6. Modular forms for congruence subgroups. 2.7. Eisenstein series for congruence subgroups. 2.8. Derivatives of modu

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