By Fred Diamond

This e-book introduces the idea 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 provides those principles, the publication states the Modularity Theorem in numerous kinds, referring to them to one another and bearing on their functions to quantity conception. The authors think no history in algebraic quantity conception and algebraic geometry. routines are included.

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