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020 _a9783319038476
_9978-3-319-03847-6
024 7 _a10.1007/978-3-319-03847-6
_2doi
035 _ato000542557
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA241-247.5
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_2bicssc
072 7 _aMAT022000
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082 0 4 _a512.7
_223
245 1 0 _aComputations with Modular Forms
_helectronic resource
_bProceedings of a Summer School and Conference, Heidelberg, August/September 2011 /
_cedited by Gebhard Böckle, Gabor Wiese.
260 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aXII, 376 p. 29 illus., 12 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aContributions in Mathematical and Computational Sciences,
_x2191-303X ;
_v6
505 0 _aPart I Summer School: Lectures on Computing Cohomology of Arithmetic Groups by P.E. Gunnells -- Computing with Algebraic Automorphic Forms by D. Loeffler -- Overconvergent Modular Symbols by R. Pollack -- Part II Conference and Research Contributions: Congruence Subgroups, Cusps and Manin Symbols over Number Fields by J. E. Cremona and M. T. Aranés -- Computing Weight One Modular Forms over C and Fp by K. Buzzard -- Lattice Methods for Algebraic Modular Forms on Classical Groups by M. Greenberg and J. Voight -- Efficient Computation of Rankin p-Adic L-Functions by A.G.B. Lauder -- Formes Modulaires Modulo 2 et Composantes Réelles de Jacobiennes Modulaires by L.Merel -- Universal Hecke L-Series Associated with Cuspidal Eigenforms over Imaginary Quadratic Fields by A. Mohamed -- On Higher Congruences Between Cusp Forms and Eisenstein Series by B. Naskrecki -- Arithmetic Aspects of Bianchi Groups by M.H.Sengün -- A Possible Generalization of Maeda’s Conjecture by P. Tsaknias -- Computing Power Series Expansions of Modular Forms by J. Voight and J. Willis -- Computing Modular Forms for GL2 over Certain Number Fields by D. Yasaki.
520 _aThis volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of the Conference and Summer School was the interplay between theory, algorithms and experiment. The 14 papers offer readers both, instructional courses on the latest algorithms for computing modular and automorphic forms, as well as original research articles reporting on the latest developments in the field. The three Summer School lectures provide an introduction to modern algorithms together with some theoretical background for computations of and with modular forms, including computing cohomology of arithmetic groups, algebraic automorphic forms, and overconvergent modular symbols. The 11 Conference papers cover a wide range of themes related to computations with modular forms, including lattice methods for algebraic modular forms on classical groups, a generalization of the Maeda conjecture, an efficient algorithm for special values of p-adic Rankin triple product L-functions, arithmetic aspects and experimental data of Bianchi groups, a theoretical study of the real Jacobian of modular curves, results on computing weight one modular forms, and more.
650 0 _amathematics.
_9566183
650 0 _aAlgebra.
_9281363
650 0 _aGeometry, algebraic.
_9303684
650 0 _aAlgorithms.
_9304813
650 0 _aNumber theory.
_9566229
650 1 4 _aMathematics.
_9566184
650 2 4 _aNumber Theory.
_9566230
650 2 4 _aAlgorithms.
_9304813
650 2 4 _aAlgebra.
_9281363
650 2 4 _aAlgebraic Geometry.
_9303686
700 1 _aBöckle, Gebhard.
_eeditor.
_9447134
700 1 _aWiese, Gabor.
_eeditor.
_9449341
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
830 0 _aContributions in Mathematical and Computational Sciences,
_9448034
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-03847-6
912 _aZDB-2-SMA
999 _c400675