By Fred Diamond,Jerry Shurman
This e-book 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 complicated 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 ebook states the Modularity Theorem in quite a few kinds, bearing on them to one another and relating their purposes to quantity thought. The authors think no history in algebraic quantity conception and algebraic geometry. workouts are included.
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Extra info for A First Course in Modular Forms (Graduate Texts in Mathematics)
A First Course in Modular Forms (Graduate Texts in Mathematics) by Fred Diamond,Jerry Shurman