By Fred Diamond,Jerry Shurman
This ebook 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 advanced 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 principles, the ebook states the Modularity Theorem in a number of kinds, referring to them to one another and referring to their purposes to quantity idea. The authors suppose no historical past 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