By Fred Diamond,Jerry Shurman
This ebook introduces the speculation of modular kinds, 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 conception; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian types linked to Hecke eigenforms. because it provides those principles, the e-book states the Modularity Theorem in a variety of varieties, referring to them to one another and pertaining to their purposes to quantity thought. The authors imagine no historical past in algebraic quantity thought 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