Description

Book Synopsis
Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. 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 it.This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.

Table of Contents
Historical Overview; Introduction to Modular Forms; Results on Finite-Dimensionality; The Arithmetic of Modular Forms; Applications of Modular Forms; Modular Forms in Characteristic p; Computing with Modular Forms; The Future of Modular Forms; Appendices on MAGMA Code for Classical Modular Forms; SAGE Code for Classical Modular Forms, Hints and Answers to the Exercises;

Modular Forms: A Classical And Computational

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    A Hardback by Lloyd James Peter Kilford

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      Book details

      Publisher Imperial College Press
      Published 29 April 2015
      ISBN-13 9781783265459
      978-1783265459
      ISBN-10 1783265450
      Also in:
      Number theory

      Description

      Book Synopsis
      Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. 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 it.This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.

      Table of Contents
      Historical Overview; Introduction to Modular Forms; Results on Finite-Dimensionality; The Arithmetic of Modular Forms; Applications of Modular Forms; Modular Forms in Characteristic p; Computing with Modular Forms; The Future of Modular Forms; Appendices on MAGMA Code for Classical Modular Forms; SAGE Code for Classical Modular Forms, Hints and Answers to the Exercises;

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