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A First Course in Modular Forms
Buch von Jerry Shurman (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung

This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. 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 intended for beginning graduate students and advanced undergraduates. It does not require background in algebraic number theory or algebraic geometry, and it contains exercises

Inhaltsverzeichnis
Modular Forms, Elliptic Curves, and Modular Curves.- Modular Curves as Riemann Surfaces.- Dimension Formulas.- Eisenstein Series.- Hecke Operators.- Jacobians and Abelian Varieties.- Modular Curves as Algebraic Curves.- The Eichler-Shimura Relation and L-functions.- Galois Representations.
Details
Erscheinungsjahr: 2005
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 472
Reihe: Graduate Texts in Mathematics
Inhalt: xvi
450 S.
57 s/w Illustr.
450 p. 57 illus.
ISBN-13: 9780387232294
ISBN-10: 038723229X
Sprache: Englisch
Herstellernummer: 10950593
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Shurman, Jerry
Diamond, Fred
Auflage: 2005
Hersteller: Springer US
Springer New York
Graduate Texts in Mathematics
Maße: 241 x 160 x 30 mm
Von/Mit: Jerry Shurman (u. a.)
Erscheinungsdatum: 19.01.2005
Gewicht: 0,955 kg
preigu-id: 102399239
Zusammenfassung

This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. 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 intended for beginning graduate students and advanced undergraduates. It does not require background in algebraic number theory or algebraic geometry, and it contains exercises

Inhaltsverzeichnis
Modular Forms, Elliptic Curves, and Modular Curves.- Modular Curves as Riemann Surfaces.- Dimension Formulas.- Eisenstein Series.- Hecke Operators.- Jacobians and Abelian Varieties.- Modular Curves as Algebraic Curves.- The Eichler-Shimura Relation and L-functions.- Galois Representations.
Details
Erscheinungsjahr: 2005
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 472
Reihe: Graduate Texts in Mathematics
Inhalt: xvi
450 S.
57 s/w Illustr.
450 p. 57 illus.
ISBN-13: 9780387232294
ISBN-10: 038723229X
Sprache: Englisch
Herstellernummer: 10950593
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Shurman, Jerry
Diamond, Fred
Auflage: 2005
Hersteller: Springer US
Springer New York
Graduate Texts in Mathematics
Maße: 241 x 160 x 30 mm
Von/Mit: Jerry Shurman (u. a.)
Erscheinungsdatum: 19.01.2005
Gewicht: 0,955 kg
preigu-id: 102399239
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