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Thursday, August 6, 2020 | History

1 edition of Computational aspects of modular forms and Galois representations found in the catalog.

Computational aspects of modular forms and Galois representations

B. Edixhoven

Computational aspects of modular forms and Galois representations

how one can compute in polynomial time the value of Ramanujan"s tau at a prime

by B. Edixhoven

  • 163 Want to read
  • 40 Currently reading

Published by Princeton University Press in Princeton .
Written in English

    Subjects:
  • Galois modules (Algebra),
  • Class field theory,
  • MATHEMATICS / Geometry / Algebraic,
  • MATHEMATICS / Advanced

  • Edition Notes

    Includes bibliographical references (p. [403]-421) and index.

    Statementedited by Bas Edixhoven and Jean-Marc Couveignes
    SeriesAnnals of mathematics studies -- 176
    Classifications
    LC ClassificationsQA247 .C638 2011
    The Physical Object
    Paginationxi, 425 p. ;
    Number of Pages425
    ID Numbers
    Open LibraryOL24882039M
    ISBN 109780691142012, 9780691142029
    LC Control Number2010053185

    Modular forms applied to the computational inverse Galois problem Johan Bosman Abstract For each of the groups PSL 2(F 25), PSL 2(F 32), PSL 2(F 49), PGL 2(F 25), and PGL 2(F 27), we display the first explicitly known polynomials over Q having that group as Galois group. Each polynomial is related to a Galois representation associated to a. of Galois representations associated to modular forms. The project has a theoretical side, proving computability and giving solid runtime analyses, and an explicit side, performing actual computations. The main contributors to the theoretical part of the project are, at this momentofwriting,BasEdixhoven,Jean-MarcCouveignes,RobindeJongandFranzMerkl.

    Get this from a library! Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM). [Jean-Marc Couveignes; Bas Edixhoven;] -- Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices.   Giving a well-informed overview of related results it will continue to be an important source of information for graduate students and researchers alike. Ch. Baxa, Wien Edixhoven, B., Couveignes, J.-M. (Eds.): Computational Aspects of Modular Forms and Galois Representations. (Annals of Mathematics Studies Vol. ).

    Get Computational Aspects of Modular Forms and Galois Representations now with O’Reilly online learning. O’Reilly members experience live online training, plus . Book chapters: Short introduction to heights and Arakelov theory (joint with Bas Edixhoven). In: J.-M. Couveignes, B. Edixhoven (eds.), Computational aspects of Modular Forms and Galois Representations. Annals of Mathematics Studies , Princeton University Press arxiv | book; Applying Arakelov theory (joint with Bas Edixhoven).


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Computational aspects of modular forms and Galois representations by B. Edixhoven Download PDF EPUB FB2

Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM) Edited by Bas Edixhoven and Jean-Marc Couveignes.

Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, - Selection from Computational Aspects of Modular Forms and Galois Representations [Book].

This is a book about computational aspects of modular forms and the Galois representations attached to them. The main result is the following: Galois representations over finite fields attached to modular forms of level one can, in almost all cases, be computed in polynomial time in the weight and the size of the finite field.

This is a book about computational aspects of modular forms and the Galois representations attached to them. The main result is the following: Galois representations over finite fields attached to. Computational Aspects of Modular Forms and Galois Representations.

Computational Aspects of Modular Forms and Galois Representations Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program.

The book begins with a concise and concrete. Abstract: This is a book about computational aspects of modular forms and the Galois representations attached to them. The main result is the following: Galois representations over finite fields attached to modular forms of level one can, in almost all cases, be computed in polynomial time in the weight and the size of the finite by: Frontmatter was published in Computational Aspects of Modular Forms and Galois Representations on page i.

The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients.

Computational aspects of modular forms and Galois representations Authors: Bas Edixhoven, Jean-Marc Couveignes, Robin de Jong, Franz Merkl, Johan Bosman Reviewer: Capi Corrales Rodrig anez,~ Department of Algebra, Mathematics, UCM, Madrid \Modular forms are functions on the complex plane which are inordinately symmetric.

They satisfy. Download PDF Abstract: This is a book about computational aspects of modular forms and the Galois representations attached to them.

The main result is the following: Galois representations over finite fields attached to modular forms of level one can, in almost all cases, be computed in polynomial time in the weight and the size of the finite field.

Chapter 8. Description of X1(5l) was published in Computational Aspects of Modular Forms and Galois Representations on page   Buy Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM) (Annals of Mathematics Studies ()) on FREE SHIPPING on qualified orders.

The material covers the theory of p-adic Galois representations and Fontaine rings, Galois deformation theory, arithmetic and computational aspects of Hilbert modular forms. Part of the Mathematical Lectures from Peking University book series (MLPKU) Abstract. In this F. Merkl, J.G. Bosman, Computational Aspects of Modular Forms and Galois Representations.

Annals of Mathematics Studies, vol. (Princeton Computations of Galois representations associated to modular forms of level one. Acta Arith. Abstract. These course notes are about computing modular forms and some of their arithmetic properties.

Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted student to implement it over any ring (such that a sufficient linear algebra theory is available in the chosen computer algebra system).

Computational Aspects of Modular Forms and Galois Representations. the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in.

Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM) (Annals of Mathematics Studies) - Kindle edition by Edixhoven, Bas, Couveignes, Jean-Marc, de Jong, Robin, Merkl, Franz, Bosman, Johan.

Download it once and read it on your Kindle device, PC, phones or cturer: Princeton University Press.

Computational aspects of modular forms and Galois representations: how one can compute in polynomial time the value of Ramanujan's tau at a prime.

[B Edixhoven; Jean-Marc Couveignes;] -- "Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Galois representations and Modular forms Bas Edixhoven July 3, Abstract These are notes for 3 lectures of hours each at the Summer School \Explicit and computational approaches to Galois representations" held at the university of Luxemburg, July The notes are based on hand written notes for a series of 4 lectures of 1.

Part one of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.

L Functions and Arithmetic LONDON MATHEMATICAL SOCIETY SYMPOSIUM ON L-FUNCTIONS AND ARITHMETIC, Durham, — in Mathematics.This banner text can have markup. web; books; video; audio; software; images; Toggle navigation.Abstract.

This is a book about computational aspects of modular forms and the Galois representations attached to them. The main result is the following: Galois representations over finite fields attached to modular forms of level one can, in almost all cases, be computed in polynomial time in the weight and the size of the finite field.