By Fred Diamond,Jerry Shurman
This publication 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 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 offers those rules, the ebook states the Modularity Theorem in a number of kinds, referring to them to one another and relating their purposes to quantity thought. The authors imagine no heritage in algebraic quantity thought and algebraic geometry. routines 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