Elliptic and Modular Functions from Gauss to Dedekind to Hecke
Published on 29. March 2017
978-1-108-13378-4 (ISBN)
Description
This thorough work presents the fundamental results of modular function theory as developed during the nineteenth and early-twentieth centuries. It features beautiful formulas and derives them using skillful and ingenious manipulations, especially classical methods often overlooked today. Starting with the work of Gauss, Abel, and Jacobi, the book then discusses the attempt by Dedekind to construct a theory of modular functions independent of elliptic functions. The latter part of the book explains how Hurwitz completed this task and includes one of Hurwitz's landmark papers, translated by the author, and delves into the work of Ramanujan, Mordell, and Hecke. For graduate students and experts in modular forms, this book demonstrates the relevance of these original sources and thereby provides the reader with new insights into contemporary work in this area.
Reviews / Votes
'Finally, it needs to be stressed that Roy does much more than present these mathematical works as museum pieces. He takes pains to tie them in to modern work when reasonable and appropriate, and that of course just adds to the quality of his work. I am very excited to have a copy of this wonderful book in my possession.' Michael Berg, MAA Reviews 'This book will be a valuable resource for understanding modular functions in their historical context, especially for readers not fluent in the languages of the original papers.' Paul M. Jenkins, Mathematical ReviewsMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
13 Line drawings, black and white
File size
4,04 MB
ISBN-13
978-1-108-13378-4 (9781108133784)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
04/2017
Cambridge University Press
€105.30
Shipment within 15-20 days
Person
Ranjan Roy is the Huffer Professor of Mathematics and Astronomy at Beloit College, Wisconsin, and has published papers in differential equations, fluid mechanics, complex analysis, and the development of mathematics. He received the Allendoerfer Prize, the Wisconsin MAA teaching award, and the MAA Haimo Award for Distinguished Mathematics Teaching, and was twice named Teacher of the Year at Beloit College. He is a co-author of three chapters in the NIST Handbook of Mathematical Functions, of Special Functions (with Andrews and Askey, Cambridge, 2010), and the author of Sources in the Development of Mathematics (Cambridge, 2011).
Content
1. The basic modular forms; 2. Gauss's contributions to modular forms; 3. Abel and Jacobi on elliptic functions; 4. Eisenstein and Hurwitz; 5. Hermite's transformation of theta functions; 6. Complex variables and elliptic functions; 7. Hypergeometric functions; 8. Dedekind's paper on modular functions; 9. The n function and Dedekind sums; 10. Modular forms and invariant theory; 11. The modular and multiplier equations; 12. The theory of modular forms as reworked by Hurwitz; 13. Ramanujan's Euler products and modular forms; 14. Dirichlet series and modular forms; 15. Sums of squares; 16. The Hecke operators.
