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Inhaltsangabe
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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Über die Autorin bzw. den Autor
Fred Diamond teaches at Brandeis University.
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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.
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A First Course in Modular Forms: 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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FIRST COURSE IN MODULAR FORMS
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A First Course in Modular Forms
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A First Course in Modular Forms
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Springer New York, Springer US Jan 2005, 2005
ISBN 10: 038723229X
ISBN 13: 9780387232294
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Buch. Zustand: Neu. Neuware -All rational elliptic curves arise from modular forms.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 472 pp. Englisch. Artikel-Nr. 9780387232294
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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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Zustand: New. 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. Artikel-Nr. 5909200
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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, Springer US, 2005
ISBN 10: 038723229X
ISBN 13: 9780387232294
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Buch. Zustand: 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. Artikel-Nr. 9780387232294
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A First Course in Modular Forms (Graduate Texts in Mathematics)
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Hardcover. Zustand: Brand New. 451 pages. 9.25x6.25x1.00 inches. In Stock. Artikel-Nr. __038723229X
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