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

By Fred Diamond,Jerry Shurman

This booklet introduces the idea of modular varieties, from which all rational elliptic curves come up, with a watch 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 concept; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian forms linked to Hecke eigenforms. because it provides those rules, the publication states the Modularity Theorem in quite a few types, concerning them to one another and concerning their purposes to quantity idea. The authors think no history in algebraic quantity idea and algebraic geometry. workouts are included.

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