5 edition of **Modular forms** found in the catalog.

Modular forms

Toshitsune Miyake

- 383 Want to read
- 30 Currently reading

Published
**1989**
by Springer-Verlag in Berlin, New York
.

Written in English

- Forms, Modular.

**Edition Notes**

Statement | Toshitsune Miyake ; [translator, Yoshitaka Maeda]. |

Classifications | |
---|---|

LC Classifications | QA243 .M6813 1989 |

The Physical Object | |

Pagination | viii, 335 p. : |

Number of Pages | 335 |

ID Numbers | |

Open Library | OL2186115M |

ISBN 10 | 0387502688 |

LC Control Number | 89004121 |

4 are each isomorphic to the Hilbert modular surface (SL 2(Z) SL 2(Z)) oZ 2 n H H: For a more detailed introduction to Siegel modular form, Humbert surfaces, and the Satake compactification of the Siegel modular threefold we refer to Freitag’s book [6]. Siegel modular forms In general, we can define the Eisenstein series. 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-.

for level 1 modular forms and use it to deduce dimension formulas and give an algorithm for explicitly computing a basis. We next introduce Hecke operators on level 1 modular forms, prove several results about them, and deduce multiplicativity of the Ramanujan τfunction as an application. We also discuss explicit computation of Hecke operators. Contents This is an introductory course into the subject of modular forms and their applications. A modular form is a complex analytic function defined on the complex upper half plane which has a certain symmetry with respect to the action of SL(2,Z) (or some subgroup) on the upper half plane and which satisfies some growth condition.

Topological Modular Forms. Christopher L. Douglas, John Francis, André G. Henriques, Michael A. Hill. This is a preliminary version of the book Topological Modular Forms published by the American Mathematical Society (AMS). BOOK REVIEWS BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Vol Number 3, July , Pages – S (06) Article electronically published on Ap A ﬁrst course in modular forms, by Fred Diamond and Jerry Shurman, Graduate Texts in Mathematics, vol. , Springer-Verlag, New York, , xvi +

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This book only assumes complex analysis and simple group theory, yet manages to cover surprisingly many modern results in the theory of modular forms.

the first 4 chapters present the basics, as covered in any intro to modular forms. but chapter 5 is a readable account of atkin-lehner theory from the '70s.

although it's not discussed in this Cited by: “The book under review is a welcome addition to the existing literature on modular forms. Being written by one of the main contributors to this subject it is designed with great care and love to detailed proofs.

Cited by: 6. Undoubtedly, due to both its breadth and readability, this book will be a useful source for mathematicians, both novice and expert, wishing to read more about modular forms and a beautiful theory." (Amanda Folsom, Bulletin of the American Mathematical Society, Vol.

46 (3), July, ). "Toshitune Miyake’s book is a useful introductory book on the subject of modular forms. Some key features of Miyake’s book are that it is accessible, well written, and well organized.

As a result, Miyake’s book is both an excellent first text from which to learn the subject and a very good : Springer-Verlag Berlin Heidelberg. 2, Hilbert and Siegel modular forms, trace formulas, p-adic modular forms, and modular abelian varieties, all of which are topics for additional books.

We also rarely analyze the complexity of the algorithms, but instead settle for occasional remarks about their practical eﬃciency.

For most of this book we assume the reader has some prior File Size: 2MB. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms.

Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Modular forms reading list1 Several textbooks and other materials are described below.

I have organized them in a hopefully helpful way. Standard textbooks First, a list of some textbooks that I would call the \main" texts for one rst learning about modular 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. “The book under review is a welcome addition to the existing literature on modular forms.

Being written by one of the main contributors to this subject it is designed with great care and love to detailed proofs. Price: $ The theory of modular forms is a fundamental tool used in many areas of mathematics and physics.

It is also a very concrete and “fun” subject in itself and abounds with an amazing number of surprising identities.

This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas.

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: Toshitsune Miyake. Elliptic Modular Forms and Their Applications 3 1 Basic Deﬁnitions 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 File Size: 1MB.

This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular.

The first three chapters provide some basic facts and results on modular forms, which set the stage for the advanced areas that are treated in the remainder of the book. Ono gives ample motivation on topics where modular forms play a role. Rather than cataloging all of the known results, he highlights those that give their flavor.

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.

This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 thro at Boston University.

Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular. 1 Introduction The study of modular forms is typically reserved for graduate students, because the amount of background needed to fully appreciate many of the constructions and methods is rather large.

However, it is possible to get a rst look at modular forms without relying too heavily on the theory of complex analysis, harmonic analysis,File Size: KB. The modular ﬁgure. Until now we considered binary forms up to the equiv-alence deﬁned by an invertible integral substitution of the variables.

We say that two binary forms are properly equivalent if they differ by a substitution with de-terminant equal to 1. In other words, we restrict ourselves with the subgroup SL(2;Z) of GL(2;Z). SinceFile Size: KB. The theory of modular forms and especially the so-called 'Ramanujan Conjectures' have been applied to resolve problems in combinatorics, computer science, analysis and number theory.

This tract, based on the Wittemore Lectures given at Yale University, is concerned with describing some of these by: 2. p-adic modular forms 20 p-adic modular forms: The Serre approach 20 The ordinary projection 24 Why p-adic modular forms are not good enough 25 3.

The canonical subgroup 26 Canonical subgroups for general p 28 The curves Xrig[r] 29 The reason everything works 31 Overconvergent p-adic modular forms 33 File Size: 1MB.

Elliptic Curves, Modular Forms and Cryptography Proceedings of the Advanced Instructional Workshop on Algebraic Number Theory. Search within book. Front Matter. Pages i-viii. PDF. Elliptic Curves. Front Matter.

Pages PDF. An overview. Modular Forms. Front Matter. Pages PDF. Introduction. B. Ramakrishnan. Pages This book is a translation of the earlier book written by Koji Doi and the author, who revised it substantially for this English edition.

It offers the basic knowledge of elliptic modular forms Read more. Rating:: (not yet rated) 0 with reviews - Be the first. Subjects: Forms, Modular.; Modulform; Vormen (wiskunde); View all subjects; More like this: Similar Items. Find a copy in the.Papers from a symposium on modular forms held 6//10/83, University of Durham, England; sponsored by the London Mathematical Society.

Description: pages: illustrations ; 24 cm.