{"product_id":"9780387232294","title":"Graduate Texts in Mathematics","description":"\u003ch1\u003eGraduate Texts in Mathematics\u003c\/h1\u003e \u003ch2\u003eDiamond, Fred; Shurman, Jerry\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cdiv\u003eThis book introduces the theory of modular forms with an eye toward the Modularity Theorem:\u003c\/div\u003eAll rational elliptic curves arise from modular forms. \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\u003cdiv\u003eThe topics covered include\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003e•\telliptic curves as complex tori and as algebraic curves,\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003e•\tmodular curves as Riemann surfaces and as algebraic curves, \u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003e•\tHecke operators and Atkin–Lehner theory, \u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003e•\tHecke eigenforms and their arithmetic properties, \u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003e•\tthe Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms, \u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003e•\telliptic and modular curves modulo p and the Eichler–Shimura Relation, \u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003e•\tthe Galois representations associated to elliptic curves and to Hecke eigenforms.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eAs it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory.\u003c\/div\u003e\u003cdiv\u003eA First Course in Modular Forms is written for beginning graduate students and advanced undergraduates. It does not require background in algebraic number theory or algebraic geometry, and it contains exercises throughout.\u003c\/div\u003e\u003cdiv\u003eFred Diamond received his Ph.D from Princeton University in 1988 under the direction of Andrew Wiles and now teaches at King's College London. Jerry Shurman received his Ph.D from Princeton University in 1988 under the direction of Goro Shimura and now teaches at Reed College.\u003c\/div\u003e\u003cdiv\u003e   \u003c\/div\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2005-01-19\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780387232294\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-0-387-27226-9\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 450\u003c\/p\u003e ","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":44499561775244,"sku":"9780387232294","price":71.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780387232294.jpg?v=1775711609","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9780387232294","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}