Fred Diamond,
Jerry Shurman
A First Course in Modular Forms
Gebonden Engels 2016 1e druk 9780387232294Levertijd ongeveer 9 werkdagen
Gratis verzonden
Samenvatting
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.
Specificaties
ISBN13:9780387232294
Taal:Engels
Bindwijze:gebonden
Aantal pagina's:436
Uitgever:Springer New York
Druk:1
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Inhoudsopgave
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.
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