000			02123 a2200301 4500
001			11575
003			IN-BhIIT
005			20260901150834.0
008			260901b |||||||| |||| 00| 0 eng d
020			_a9781441920058 (paperback)
040			_aIN-BhIIT
041			_aeng
082			_a511.381 _bDIA/F
100			_aDiamond, Fred. _eauthor _928556
245			_aA first course in modular forms / _cFred Diamond and Jerry Shurman.
260			_aNew York : _bSpringer, _c2010.
300			_axv, 436 pages : _billustrations ; _c23 cm.
490			_aGraduate texts in mathematics ; volume 228
504			_aIncludes bibliographical references and index.
505			_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.
520			_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.
650			_aForms, Modular. _921664
650			_aModular forms. _928557
650			_aElliptic functions. _910211
650			_aNumber theory.
700			_aShurman, Jerry Michael. _eJoint author _928558
942			_cTRB
999			_c15706 _d15706