02282    a2200313   450000100060000000300090000600500170001500800410003202000300007304000130010304100080011608200190012410000340014324500710017726000330024830000450028149000470032650400510037350503830042452008370080765000270164465000260167165000310169765000190172870000490174794200080179699900170180495201470182111575IN-BhIIT20260901150834.0260901b        |||||||| |||| 00| 0 eng d  a9781441920058 (paperback)  aIN-BhIIT  aeng  a511.381bDIA/F  aDiamond, Fred.eauthor928556  aA first course in modular forms /cFred Diamond and Jerry Shurman.  aNew York :bSpringer,c2010.  axv, 436 pages :billustrations ;c23 cm.  aGraduate texts in mathematics ; volume 228  aIncludes bibliographical references and index.  aModular forms, elliptic curves, and modular curves -- Modular curves as Riemann surfaces -- Dimension formulas -- Eisenstein series -- Hecke operators -- Jacobians and abelian varieties -- Modular curves as algebraic curves -- The Eichler-Shimura relation and L-functions -- Galois representations -- Hints and answers to the exercises -- List of symbols -- Index -- References.  aA first course in modular forms: This textbook introduces the theory of modular forms and explains their deep connections with elliptic curves, modular curves, and modern number theory. The authors develop the subject from fundamental concepts through modular curves as Riemann surfaces and algebraic curves, dimension formulas, Eisenstein series, Hecke operators, Hecke eigenforms, Jacobians and Abelian varieties, the Eichler-Shimura relation, L-functions, and Galois representations. A major objective is to explain the Modularity Theorem and its relationship to rational elliptic curves. Designed for advanced undergraduates and beginning graduate students, the book provides a largely self-contained treatment, includes exercises throughout, and does not assume prior knowledge of algebraic number theory or algebraic geometry.  aForms, Modular.921664  aModular forms.928557  aElliptic functions.910211  aNumber theory.  aShurman, Jerry Michael.eJoint author928558  cTRB  c15706d15706  00102ddc40708SBSaCLIITBBSbCLIITBBScTRBd2026-08-28e21g5224.87l0o511.381 DIA/Fp11575r2026-08-28 00:00:00v7157.35w2026-08-28yTRB