By Fred Diamond,Jerry Shurman
This e-book introduces the speculation 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 conception; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian forms linked to Hecke eigenforms. because it offers those rules, the e-book states the Modularity Theorem in numerous types, touching on them to one another and referring to their functions to quantity idea. The authors suppose no heritage in algebraic quantity thought and algebraic geometry. workouts are included.
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Additional 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