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Computations with modular forms : proceedings of a summer school and conference, Heidelberg, August/September 2011

Author: Gebhard Böckle; Gabor Wiese
Publisher: Heidelberg : Springer, [2014]
Series: Contributions in mathematical and computational sciences, 6.
Edition/Format:   eBook : Document : Conference publication : EnglishView all editions and formats
Summary:
This 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  Read more...
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Genre/Form: Electronic books
Conference papers and proceedings
Congresses
Additional Physical Format: Print version:
Computations With Modular Forms
(OCoLC)865495668
Material Type: Conference publication, Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Gebhard Böckle; Gabor Wiese
ISBN: 9783319038476 3319038478
OCLC Number: 869376414
Description: 1 online resource
Contents: Part 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.
Series Title: Contributions in mathematical and computational sciences, 6.
Responsibility: Gebhard Böckle, Gabor Wiese, editors.

Abstract:

This 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.

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