By Fred Diamond,Jerry Shurman

This ebook introduces the speculation of modular types, from which all rational elliptic curves come up, with a watch towards the Modularity Theorem. dialogue covers elliptic curves as advanced tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner idea; Hecke eigenforms and their mathematics houses; the Jacobians of modular curves and the Abelian forms linked to Hecke eigenforms. because it offers those principles, the e-book states the Modularity Theorem in quite a few kinds, concerning them to one another and bearing on their purposes to quantity thought. The authors suppose no heritage in algebraic quantity concept and algebraic geometry. routines are included.

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