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

Libro 37 de 180: Graduate Texts in Mathematics

Diamond, Fred; Shurman, Jerry

 
9780387232294: A First Course in Modular Forms: 228 (Graduate Texts in Mathematics)
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ISBN 10: 038723229X ISBN 13: 9780387232294
Editorial: Springer, 2007

Sinopsis

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.

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Acerca del autor

Fred Diamond teaches at Brandeis University.

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 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.
   

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Editorial
Springer
Año de publicación
2007
Idioma
Inglés
ISBN 10 
038723229X
ISBN 13 
9780387232294
Encuadernación
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Número de edición
1
Número de páginas
456
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Otras ediciones populares con el mismo título

9781441920058: A First Course in Modular Forms: 228 (Graduate Texts in Mathematics)

Edición Destacada

ISBN 10:  1441920056 ISBN 13:  9781441920058
Editorial: Springer, 2010
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