A First Course in Modular Forms

Jerry Shurman

ISBN 10: 1441920056 / ISBN 13: 9781441920058

Editore: Springer New York, Springer US, 2010

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9781441920058

Dati bibliografici

• Titolo: A First Course in Modular Forms
• Editore: Springer New York, Springer US
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 1441920056
• ISBN 13: 9781441920058
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 24 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 24 millimetri di profondità
• Peso: 795 grammi

Descrizione articolo

Riassunto

This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. The Theorem is stated in various forms, related to each other and to their applications to number theory.

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 Brandeis University. Jerry Shurman received his Ph.D from Princeton University in 1988 under the direction of Goro Shimura and now teaches at Reed College.