A First Course in Modular Forms: 228 (Graduate Texts in Mathematics) - Tapa blanda

Diamond, Fred

 
9781441920058: A First Course in Modular Forms: 228 (Graduate Texts in Mathematics)
Tapa blanda
ISBN 10: 1441920056 ISBN 13: 9781441920058
Editorial: Springer, 2010

Sinopsis

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.

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De la contraportada

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2010
Idioma
Inglés
ISBN 10 
1441920056
ISBN 13 
9781441920058
Encuadernación
Tapa blanda
Número de páginas
472
Contacto del fabricante
no disponible
Persona responsable
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Hamburg
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Otras ediciones populares con el mismo título

9780387232294: A First Course in Modular Forms: 228 (Graduate Texts in Mathematics)

Edición Destacada

ISBN 10:  038723229X ISBN 13:  9780387232294
Editorial: Springer, 2007
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