By Fred Diamond,Jerry Shurman
This booklet introduces the speculation of modular varieties, from which all rational elliptic curves come up, with an eye fixed 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 booklet states the Modularity Theorem in numerous types, concerning them to one another and concerning their functions to quantity conception. The authors imagine no historical past in algebraic quantity conception and algebraic geometry. routines are included.
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A First Course in Modular Forms (Graduate Texts in Mathematics) by Fred Diamond,Jerry Shurman