A First Course in Modular Forms

Jerry Shurman, Fred Diamond

ISBN 10: 038723229X / ISBN 13: 9780387232294

Editore: Springer-Verlag New York Inc., US, 2005

Riguardo questo articolo

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 eigenformsAs 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.

Codice articolo LU-9780387232294

Dati bibliografici

• Titolo: A First Course in Modular Forms
• Editore: Springer-Verlag New York Inc., US
• Data di pubblicazione: 2005
• Lingua: Inglese
• ISBN 10: 038723229X
• ISBN 13: 9780387232294
• Rilegatura: Hardback
• Edizione: 1st ed. 2005. Corr. 3nd printing 2007.
• Condizione: New

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

Fred Diamond teaches at Brandeis University.