Introduction to the Construction of Class Fields PDF Download
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Author: Harvey Cohn
Publisher: Courier Corporation
ISBN: 9780486683461
Category : Mathematics
Languages : en
Pages : 244
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Book Description
A broad introduction to quadratic forms, modular functions, interpretation by rings and ideals, class fields by radicals and more. 1985 ed.
Author: Harvey Cohn
Publisher: Courier Corporation
ISBN: 9780486683461
Category : Mathematics
Languages : en
Pages : 244
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Book Description
A broad introduction to quadratic forms, modular functions, interpretation by rings and ideals, class fields by radicals and more. 1985 ed.
Author: Harvey Cohn
Publisher: CUP Archive
ISBN: 9780521247627
Category : Mathematics
Languages : en
Pages : 232
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Book Description
In this graduate level textbook, Professor Cohn takes a problem that Pythagoras could have posed, and using it as motivation, develops a constructional introduction to classical field theory and modular function theory. The interest in constructional techniques has increased recently with the advent of cheap and plentiful computer technology. The beginning chapters provide the motivation and necessary background in elementary algebraic number theory and Riemann surface theory. The ideas and results are then applied and extended to class field theory. In the later chapters, more specialized results are presented, with full proofs, though the author emphasizes, with examples, the relation of the material to other parts of mathematics.
Author: Georges Gras
Publisher: Springer Science & Business Media
ISBN: 3540441336
Category : Mathematics
Languages : en
Pages : 513
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Book Description
Global class field theory is a major achievement of algebraic number theory based on the functorial properties of the reciprocity map and the existence theorem. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.
Author: David A. Cox
Publisher: American Mathematical Soc.
ISBN: 1470470284
Category : Education
Languages : en
Pages : 551
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Book Description
This book studies when a prime p can be written in the form x2+ny2. It begins at an elementary level with results of Fermat and Euler and then discusses the work of Lagrange, Legendre and Gauss on quadratic reciprocity and the genus theory of quadratic forms. After exploring cubic and biquadratic reciprocity, the pace quickens with the introduction of algebraic number fields and class field theory. This leads to the concept of ring class field and a complete but abstract solution of p=x2+ny2. To make things more concrete, the book introduces complex multiplication and modular functions to give a constructive solution. The book ends with a discussion of elliptic curves and Shimura reciprocity. Along the way the reader will encounter some compelling history and marvelous formulas, together with a complete solution of the class number one problem for imaginary quadratic fields. The book is accessible to readers with modest backgrounds in number theory. In the third edition, the numerous exercises have been thoroughly checked and revised, and as a special feature, complete solutions are included. This makes the book especially attractive to readers who want to get an active knowledge of this wonderful part of mathematics.
Author: Wladyslaw Narkiewicz
Publisher: Springer Science & Business Media
ISBN: 3662070014
Category : Mathematics
Languages : en
Pages : 712
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Book Description
This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.
Author: Attila Pethoe
Publisher: Walter de Gruyter
ISBN: 3110865955
Category : Mathematics
Languages : en
Pages : 357
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Book Description
Author: Seifallah Randjbar-daemi
Publisher: World Scientific
ISBN: 981461145X
Category :
Languages : en
Pages : 322
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Book Description
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Publisher:
ISBN:
Category : Greek letter societies
Languages : en
Pages : 704
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Book Description
Author: Bimal Kumar Roy
Publisher: Springer
ISBN: 3540444955
Category : Computers
Languages : en
Pages : 306
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Book Description
The field of Cryptology witnessed a revolution in the late seventies. Since then it has been expanded into an important and exciting area of research. Over the last two decades, India neither participated actively nor did it contribute sig nificantly towards the development in this field. However, recently a number of active research groups engaged in important research and developmental work have crystalized in different parts of India. As a result, their interaction with the international crypto community has become necessary. With this backdrop, it was proposed that a conference on cryptology - INDOCRYPT, be organized for the first time in India. The Indian Statistical Institute was instrumental in hosting this conference. INDOCRYPT has generated a large amount of enthu siasm amongst the Indians as well as the International crypto communities. An INDOCRYPT steering committee has been formed and the committee has plans to make INDOCRYPT an annual event. For INDOCRYPT 2000, the program committee considered a total of 54 pa pers and out of these 25 were selected for presentation. The conference program also included two invited lectures by Prof. Adi Shamir and Prof. Eli Biham. These proceedings include the revised versions of the 25 papers accepted by the program committee. These papers were selected from all the submissions based on originality, quality and relevance to the field of Cryptology. Revisions were not checked and the authors bear the full responsibility for the contents of the papers in these proceedings.
Author: Hugh C. Williams
Publisher: American Mathematical Soc.
ISBN: 9780821887592
Category : Science
Languages : en
Pages : 412
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Book Description
This volume consists of a selection of papers based on presentations made at the international conference on number theory held in honor of Hugh Williams' sixtieth birthday. The papers address topics in the areas of computational and explicit number theory and its applications. The material is suitable for graduate students and researchers interested in number theory.
