7 edition of **Introduction to Modular Forms (Grundlehren Der Mathematischen Wissenschaften, No 222)** found in the catalog.

- 86 Want to read
- 3 Currently reading

Published
**July 1995**
by Springer
.

Written in English

The Physical Object | |
---|---|

Number of Pages | 261 |

ID Numbers | |

Open Library | OL7442581M |

ISBN 10 | 0387078339 |

ISBN 10 | 9780387078335 |

Published on Dec 6, “Introduction to Modular Forms,” by Keith Conrad. Topics include Eisenstein series and q-expansions, applications to sums of squares and zeta-values, Hecke operators. The theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections with number theory. Modular forms appear in other areas, such as algebraic topology, sphere packing, and string theory.

About this Book: MBI along with Clemson University developed “Introduction to Commercial Modular Construction” over two years with the goal of introducing the reader to an innovative and exciting construction method. This book discusses the modular building process compared to traditional site-built construction and is designed to helpFile Size: KB. 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.

Automorphic forms Modular forms are a special case of automorphic forms. These more general objects are very important tools these days in number theory. Gelbart, Automorphic forms on adele groups: an excellent book that begins by reviewing relevant facts about classical modular forms and then explains the transition to automorphic forms and representa-File Size: KB. 5. Siegel modular forms 33 De nitions and examples of Siegel modular forms 33 Quantum black holes and Siegel modular forms 36 6. Walls and contours 37 7. Mock modular forms 40 Pure mock modular forms 40 Mock Jacobi forms 44 Mock modular forms: the general case 48 Superconformal characters and mock modular forms 50 Size: 1MB.

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Lang makes no claim to provide in his book a comprehensive introduction to the huge field that is modular forms. As with most books, this one would be well complemented by certain others,especially given the vast array of results and approaches to the field.

It is true that Lang includes few by: Introduction to Modular Forms (Grundlehren der mathematischen Wissenschaften Book ) - Kindle edition by Lang, Serge. Download it once and read it on your Kindle device, PC, phones or tablets.

Use features like bookmarks, note taking and highlighting while reading Introduction to Modular Forms (Grundlehren der mathematischen Wissenschaften Book ).4/5(1). Usually dispatched within 3 to 5 business days.

From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form.

Complete and readable proofs are given. Introduction From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms.

Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given.

The opening chapters define modular forms, develop their most important properties, and introduce the Hecke modular forms. Subsequent chapters explore the automorphisms of a compact Riemann surface, develop congruences and other arithmetic properties for the Fourier coefficients of Klein's absolute modular invariant, 5/5(3).

assigned from this book (among other resources). (2)Serre, A Course in Arithmetic. The last part of this book has a concise explanation of modular forms for SL 2(Z). (3)Shimura, Introduction to the Arithmetic Theory of Automorphic Functions. (4)Lang, Introduction to Modular Forms.

Basic De nitions. We begin with some basic de nitions. As it Introduction to Modular Forms book these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory.A First Course in Modular Forms is written for beginning graduate students and advanced undergraduates.

"This introduction to modular forms is aimed at students with only a basic knowledge of complex function theory.

A useful and up-to-date exposition of topics scattered throughout the literature, aided by exercises with answers." (Mathematika, Vol.

52, )Cited by: In this section we introduce the basic objects of study – the group SL(2,R) and its action on the upper half plane, the modular group, and holomorphic modular forms – and show that the space of modular forms of any weight and level is ﬁnite-dimensional.

This File Size: 1MB. These notes serve as an explicit introduction to theory of modular forms. It is intended to give a precise introduction about the most important concepts in the theory of modular forms and the recent developments on the theory of period polynomials emerging from modular forms on the full modular group.

Period poly. Modular forms. To construct a modular function, we have to construct a meromorphic function on H that is invariant under the action of.N/. This is difﬁcult.

It is easier to construct functions that transform in a certain way under the action of.N/ ; the quotient of two such functions of same type will then be a modular Size: KB. INTRODUCTION TO MODULAR FORMS Introduction Modular forms arose in association to the elliptic funcions in the early 19th century.

Nowadays the Galois rapresentation associated to modular forms play a central role in the modern Number Theory.

A goal in Number Theory is to understand the nite extensions of Q, and by Galois Thepry thisFile Size: KB. As a result, Miyake’s book is both an excellent first text from which to learn the subject and a very good reference. I have found myself returning to the book repeatedly for tidbits that are hard to find in the literature.

Miyake’s book is an excellent introduction to modular forms." (Eknath Ghate, SIAM Review, Vol. 48 (3), )Brand: Springer-Verlag Berlin Heidelberg. Books 7 1. Preliminaries 8 Continuousgroupactions. 8 Riemannsurfaces: classicalapproach 10 MODULAR FUNCTIONS AND MODULAR FORMS 1.

Introduction Itis easy to deﬁne modular functions and forms, but lesseasy to say why they are important, especiallyto numbertheorists. ThusI will beginwitha rather long.

The first one: 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 second one: The advanced one "Modular forms" by Toshitsune Miyake is also a very good textbook to learn modular forms.

The more advanced books, you can consider to read the books by. The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory.

This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse Cited by: This book gives a beautiful introduction to the theory of modular forms, with a delicate balance of analytic and arithmetic perspectives.

Cohen and Strömberg start with a foundational collection of tools in analysis and number theory, which they use while guiding the reader through a vast landscape of results. Authors: Koblitz, Neal I. Usually dispatched within 3 to 5 business days.

Usually dispatched within 3 to 5 business days. This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. "Introduction to Siegel Modular Forms and Dirichlet Series is a compact but masterful presentation of this important generalization of the classical theory, and a good deal more.

beneficiaries of this wonderful book are the obvious candidates: students of number theory with their qualifying examinations behind them, or very gifted Brand: Springer-Verlag New York. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory.

A First Course in Modular Forms is written for beginning graduate students and advanced undergraduates. An Introduction to Modular Forms Henri Cohen Abstract In this course we introduce the main notions relative to the classical theory of mod-ular forms.

A complete treatise in a similar style can be found in the author’s book joint with F. Str¨omberg [1]. 1 Functional Equations Let f be a complex function deﬁned over some subset D of C.

Title: An Introduction to Modular Forms. Authors: Henri Cohen (LFANT) (Submitted on 28 Sep ) 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 F. Str{ö}mberg [1]. Subjects: Number Theory ()Author: Henri Cohen.Nathan C. Ryan A Motivated Introduction to Modular Forms Lagrange’s Four Squares Theorem InLagrange proved Every integer can be written as the sum of 4 Size: 2MB.