The Web of Modularity (CBMS Regional Conference Series in Mathematics): Arithmetic of the Coefficients of Modular Forms and Q-Series - Softcover

American Mathematical Society

Softcover

ISBN 10: 0821833685 ISBN 13: 9780821833681

Publisher: American Mathematical Society, 2004

Synopsis

Modular forms appear in many ways in number theory. They play a central role in the theory of quadratic forms, in particular, as generating functions for the number of representations of integers by positive definite quadratic forms. They are also key players in the recent spectacular proof of Fermat's Last Theorem. Modular forms are at the center of an immense amount of current research activity. Also detailed in this volume are other roles that modular forms and $q$-series play in number theory, such as applications and connections to basic hypergeometric functions, Gaussian hypergeometric functions, super-congruences, Weierstrass points on modular curves, singular moduli, class numbers, $L$-values, and elliptic curves.The first three chapters provide some basic facts and results on modular forms, which set the stage for the advanced areas that are treated in the remainder of the book. Ono gives ample motivation on topics where modular forms play a role. Rather than cataloging all of the known results, he highlights those that give their flavor. At the end of most chapters, he gives open problems and questions. The book is an excellent resource for advanced graduate students and researchers interested in number theory.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2004
• Language: English
• ISBN 10: 0821833685
• ISBN 13: 9780821833681
• Binding: Paperback
• Number of pages: 216