By Fred Diamond,Jerry Shurman
This publication introduces the idea of modular kinds, 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 houses; the Jacobians of modular curves and the Abelian forms linked to Hecke eigenforms. because it offers those rules, the booklet states the Modularity Theorem in a number of kinds, concerning them to one another and pertaining to their purposes to quantity thought. The authors suppose no history in algebraic quantity conception and algebraic geometry. routines are included.
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Extra resources 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