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 houses; 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 types, bearing on them to one another and referring to their functions to quantity thought. The authors imagine no history in algebraic quantity idea 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