000 03124nam a22004695i 4500
001 978-0-387-27226-9
003 DE-He213
005 20161121230924.0
007 cr nn 008mamaa
008 100301s2005 xxu| s |||| 0|eng d
020 _a9780387272269
_9978-0-387-27226-9
024 7 _a10.1007/b138781
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
082 0 4 _a512.7
_223
100 1 _aDiamond, Fred.
_eauthor.
245 1 2 _aA First Course in Modular Forms
_h[electronic resource] /
_cby Fred Diamond, Jerry Shurman.
264 1 _aNew York, NY :
_bSpringer New York,
_c2005.
300 _aXVI, 436 p. 29 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v228
505 0 _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. .
520 _aThis book introduces the theory of modular forms with an eye toward the Modularity Theorem: All rational elliptic curves arise from modular forms. The topics covered include • elliptic curves as complex tori and as algebraic curves, • modular curves as Riemann surfaces and as algebraic curves, • Hecke operators and Atkin–Lehner theory, • Hecke eigenforms and their arithmetic properties, • the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms, • elliptic and modular curves modulo p and the Eichler–Shimura Relation, • the Galois representations associated to elliptic curves and to Hecke eigenforms. As 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. A 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. Fred 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. .
650 0 _aMathematics.
650 0 _aAlgebraic geometry.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aNumber Theory.
650 2 4 _aAlgebraic Geometry.
700 1 _aShurman, Jerry.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387232294
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v228
856 4 0 _uhttp://dx.doi.org/10.1007/b138781
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c505975
_d505975