A First Course in Modular Forms (Graduate Texts in by Fred Diamond,Jerry Shurman

By Fred Diamond,Jerry Shurman

This ebook introduces the idea of modular varieties, from which all rational elliptic curves come up, with an eye fixed towards the Modularity Theorem. dialogue covers elliptic curves as complicated tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner thought; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian types linked to Hecke eigenforms. because it offers those rules, the ebook states the Modularity Theorem in numerous varieties, referring to them to one another and bearing on their purposes to quantity concept. The authors think no historical past in algebraic quantity conception and algebraic geometry. routines are included.

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