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Tuesday, May 5, 2020 | History

14 edition of Modular forms, a computational approach found in the catalog.

Modular forms, a computational approach

by William A. Stein

  • 307 Want to read
  • 35 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Forms, Modular -- Data processing -- Textbooks,
  • Algebraic spaces -- Data processing -- Textbooks

  • Edition Notes

    Includes bibliographical references (p. 253-264) and index

    StatementWilliam Stein ; with an appendix by Paul E. Gunnells
    GenreTextbooks
    SeriesGraduate studies in mathematics -- v. 79
    Classifications
    LC ClassificationsQA243 .S74 2007
    The Physical Object
    Paginationxv, 268 p. :
    Number of Pages268
    ID Numbers
    Open LibraryOL17218133M
    ISBN 100821839608
    ISBN 109780821839607
    LC Control Number2006047950

    MODULAR FORMS - A COMPUTATIONAL APPROACH 1 2 1 A fundamental domain of a nite index subgroup of SL 2(Z) Modular forms play an important role in number theory, algebraic geometry and physics. Using new tools from an open source project called SAGE[SAG] it possible to access a wealth of information about the module space. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from second edition has.

      Arithmetic is a generally difficult subject for which we have few techniques available. Modular forms have the good taste of being reasonably computable. For the full group [math]SL_2(Z)[/math] this is Modular form. For other subgroups of [math]SL. The book"A first course in modular forms" by F. Diamond, J. Shurman is a good book to start to study classical modular forms. The advanced one "Modular forms" by Toshitsune Miyake is also a very good textbook to learn modular forms. Good luck.

    Chapter Four Short introduction to heights and Arakelov theory. by Bas Edixhoven and Robin de Jong Chapter 3 explained how the computation of the Galois representations V attached to modular forms over finite fields should proceed. The essential step is to approximate the minimal polynomial P of () with sufficient precision so that P itself can be obtained. Chapter Twelve Approximating Vƒ over the complex numbers by Jean-Marc Couveignes In this chapter, we address the problem of computing torsion divisors on modular curves with an application to - Selection from Computational Aspects of Modular Forms and Galois Representations [Book].


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Modular forms, a computational approach by William A. Stein Download PDF EPUB FB2

2(Z) and modular forms as functions on the complex upper half plane. We discuss q-expansions, which provide an important computational handle on modular forms. We also Modular forms an algorithm for computing with congruence subgroups.

The chapter ends with a list File Size: 2MB. The author, a leading expert in the field of computational arithmetic, presents here the first comprehensive textbook about algorithms for computing with modular forms, together with an accompanying introduction to the underlying theory of modular forms.

Book News Inc. "The author, a leading expert in the field of computational arithmetic, presents here the first comprehensive textbook about algorithms for computing with modular forms, together with an accompanying introduction to the underlying theory of modular forms.

Cited by: Modular Forms, a Computational Approach (Graduate Studies in Mathematics) by William Stein () [Stein, William;Gunnells, Paul E.] on *FREE* shipping on qualifying offers.

Modular Forms, a Computational Approach (Graduate Studies in Mathematics) by William Stein ()Author: Paul E. Stein, William;Gunnells. Modular forms, a computational approach. [William A Stein] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for Covers classical modular forms.

This book is suitable to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. Modular Forms: A Computational Approach by William A. Stein. Publisher: American Mathematical Society ISBN/ASIN: ISBN Number of pages: Description: Modular forms marvellous and highly original book fills a significant gap.

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).

Modular forms, a computational approach / William Stein ; with an appendix by Paul E. Gunnells. — (Graduate studies in mathematics ; v. 79) Includes bibliograpical references and index. ISBN (alk. paper) 1. Forms, Modular—Data processing—Textbooks.

Algebraic spaces—Data processing— Textbooks. Title Cited by: Modular forms, a computational approach. [William A Stein] Covers classical modular forms. This book is suitable to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations.

Modular forms Modular forms of level $1$ Modular forms of weight $2$ Dirichlet characters Eisenstein series. Destination page number Search scope Search Text Search scope Search Text. William Stein was one such; his Modular Forms, a Computational Approach is an attempt to teach us all how to do it.

While the book does explain the basic theory, Stein warns the reader that the focus is really not on the underlying ideas and theorems. and modular forms as functions on the complex upper half plane.

We discuss q-expansions, which provide an important computational handle on modular forms. We also study an algorithm for computing with congruence subgroups.

The chap-ter ends with a list of applications of modular forms throughout mathematics. In Chapter 2 we discuss level 1. Modular Forms, a Computational Approach William Stein Publication Year: ISBN ISBN Graduate Studies in Mathematics, vol.

Modular forms can actually be viewed as elements in the group cohomolgy of discrete subgroups of SL(2;R). This is what allows us to compute with them in Sage, etc. Stein, Modular forms: a computational approach: this book is in fact an alternative for a basic textbook on modular forms.

Abstract. In this course, we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author’s book joint with Strömberg (Cohen and Strömberg, Modular Forms: A Classical Approach, Graduate Studies in Math.American Math.

Soc. () []). A complete treatise in a similar style can be found in the author’s book joint with Strömberg (Cohen and Strömberg, Modular Forms: A Classical Approach, Graduate Studies in Math. American. Modular Forms, a Computational Approach About this Title.

William Stein, University of Washington, Seattle, WA. Publication: Graduate Studies in Mathematics Publication Year Volume 79 ISBNs: (print); (online). Modular Forms: A Computational Approach (free online book) or buy it from the AMS or buy it from ; with an appendix by Paul Gunnells ( pages), AMS Graduate Studies in.

$\begingroup$ Another good reference is the springer book \textit{A first course in modular forms} of Diamond and Shurman. Or if you wish something more algebraic, you can have a look at the paper of Diamond and Im entitled \textit{Modular forms and modular curves}. $\endgroup$ – Nicolas B.

Koop Modular forms, a computational approach van Stein, w. met ISBN Gratis verzending, Slim studeren. I am reading William A. Stein's book "Modular Forms: A Computational Approach".

In Chapter 3 of this book, he studies Modular Forms of Weight 2. One can also refer to the following website about this Chapter.

Modular Forms of Weight 2.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 .( views) Modular Forms: A Computational Approach by William A.

Stein - American Mathematical Society, This book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional.