A First Course in Modular Forms (Graduate Texts in Mathematics, 228, Band 228)

Diamond, Fred and Jerry Shurman:

ISBN 10: 038723229X / ISBN 13: 9780387232294

Published by Springer., 2005

About this Item

436 Seiten, mit Abbildungen, Zust: Gutes Exemplar. Schneller Versand und persönlicher Service - jedes Buch händisch geprüft und beschrieben - aus unserem Familienbetrieb seit über 25 Jahren. Eine Rechnung mit ausgewiesener Mehrwertsteuer liegt jeder unserer Lieferungen bei. Wir versenden mit der deutschen Post. Sprache: Englisch Gewicht in Gramm: 770.

Seller Inventory # 360147

Bibliographic Details

• Title: A First Course in Modular Forms (Graduate Texts in Mathematics, 228, Band 228)
• Publisher: Springer.
• Publication Date: 2005
• Language: English
• ISBN 10: 038723229X
• ISBN 13: 9780387232294
• Binding: Karton Karton
• Condition: Sehr gut
• Weight: 770 grams
• Seller catalogs:
  • Mathematik

About this title

Synopsis

This book introduces the theory of modular forms with an eye toward the Modularity Theorem:

All rational elliptic curves arise from modular forms.

The topics covered include

• elliptic curves as complex tori and as algebraic curves,

• modular curves as Riemann surfaces and as algebraic curves, 

• Hecke operators and Atkin–Lehner theory, 

• Hecke eigenforms and their arithmetic properties, 

• the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms, 

• elliptic and modular curves modulo p and the Eichler–Shimura Relation, 

• the Galois representations associated to elliptic curves and to Hecke eigenforms.

As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory.

A First Course in Modular Forms is written for beginning graduate students and advanced undergraduates. It does not require background in algebraic number theory or algebraic geometry, and it contains exercises throughout.

Fred Diamond received his Ph.D from Princeton University in 1988 under the direction of Andrew Wiles and now teaches at King's College London. Jerry Shurman received his Ph.D from Princeton University in 1988 under the direction of Goro Shimura and now teaches at Reed College.

   

About the Author

Fred Diamond teaches at Brandeis University.