By Fred Diamond

This booklet introduces the idea of modular types, from which all rational elliptic curves come up, with an eye fixed 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 homes; the Jacobians of modular curves and the Abelian types linked to Hecke eigenforms. because it provides those principles, the ebook states the Modularity Theorem in a variety of varieties, touching on them to one another and concerning their functions to quantity conception. The authors think no history in algebraic quantity thought and algebraic geometry. routines are included.

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