A First Course in Modular Forms: 228 - Rilegato

Diamond, Fred; Sturmfels, Bernd; Shurman, Jerry Michael

Rilegato

ISBN 10: 038723229X ISBN 13: 9780387232294

Casa editrice: Springer Nature, 2005

Riassunto

This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers 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. 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. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.

Su questo libro

Informazioni sull'autore

Fred Diamond teaches at Brandeis University.

Dalla quarta di copertina

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.

   

Dettagli dell'edizione

• Editore: Springer Nature
• Data di pubblicazione: 2005
• Lingua: Inglese
• ISBN 10: 038723229X
• ISBN 13: 9780387232294
• Rilegatura: Copertina rigida
• Numero di pagine: 472
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3,69115 Heidelberg, Germany; Heidelberg; 69115; Germania