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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,
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.
"Sobre este título" puede pertenecer a otra edición de este libro.
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A First Course in Modular Forms (Graduate Texts in Mathematics, Vol. 228) (Graduate Texts in Mathematics, 228)
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A First Course in Modular Forms (Graduate Texts in Mathematics, Vol. 228) (Graduate Texts in Mathematics, 228)
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A First Course in Modular Form
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A First Course in Modular Forms (Graduate Texts in Mathematics, Vol. 228) (Graduate Texts in Mathematics, 228)
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A First Course in Modular Forms
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Springer New York Jan 2005, 2005
ISBN 10: 038723229X
ISBN 13: 9780387232294
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Librería: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Alemania
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Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 472 pp. Englisch. Nº de ref. del artículo: 9780387232294
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A First Course in Modular Forms
Impresión bajo demandaLibrería: moluna, Greven, Alemania
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Covers many topics not covered in other texts on elliptic curvesCovers many topics not covered in other texts on elliptic curvesIncludes supplementary material: sn.pub/extrasThis book introduces the theory of modular forms, from whi. Nº de ref. del artículo: 5909200
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A First Course in Modular Forms
Publicado por
Springer New York, Springer US, 2005
ISBN 10: 038723229X
ISBN 13: 9780387232294
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Librería: AHA-BUCH GmbH, Einbeck, Alemania
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Buch. Condición: Neu. 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. Nº de ref. del artículo: 9780387232294
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A First Course in Modular Forms
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A First Course in Modular Forms
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Condición: New. pp. 456 Illus. This item is printed on demand. Nº de ref. del artículo: 7596808
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