Introduction To The Construction Of Class Fields
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Introduction To The Construction Of Class Fields
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Author : Harvey Cohn
language : en
Publisher: Courier Corporation
Release Date : 1994-01-01
Introduction To The Construction Of Class Fields written by Harvey Cohn and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.
A broad introduction to quadratic forms, modular functions, interpretation by rings and ideals, class fields by radicals and more. 1985 ed.
Introduction To The Construction Of Class Fields
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Author : Harvey Cohn
language : en
Publisher: CUP Archive
Release Date : 1985-08-30
Introduction To The Construction Of Class Fields written by Harvey Cohn and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-08-30 with Mathematics categories.
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.
Elementary And Analytic Theory Of Algebraic Numbers
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Author : Wladyslaw Narkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Elementary And Analytic Theory Of Algebraic Numbers written by Wladyslaw Narkiewicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
The aim of this book is to present an exposition of the theory of alge braic numbers, excluding class-field theory and its consequences. There are many ways to develop this subject; the latest trend is to neglect the classical Dedekind theory of ideals in favour of local methods. However, for numeri cal computations, necessary for applications of algebraic numbers to other areas of number theory, the old approach seems more suitable, although its exposition is obviously longer. On the other hand the local approach is more powerful for analytical purposes, as demonstrated in Tate's thesis. Thus the author has tried to reconcile the two approaches, presenting a self-contained exposition of the classical standpoint in the first four chapters, and then turning to local methods. In the first chapter we present the necessary tools from the theory of Dedekind domains and valuation theory, including the structure of finitely generated modules over Dedekind domains. In Chapters 2, 3 and 4 the clas sical theory of algebraic numbers is developed. Chapter 5 contains the fun damental notions of the theory of p-adic fields, and Chapter 6 brings their applications to the study of algebraic number fields. We include here Shafare vich's proof of the Kronecker-Weber theorem, and also the main properties of adeles and ideles.
A First Course In Partial Differential Equations With Complex Variables And Transform Methods
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Author : Hans F. Weinberger
language : en
Publisher: Courier Corporation
Release Date : 1995-01-01
A First Course In Partial Differential Equations With Complex Variables And Transform Methods written by Hans F. Weinberger and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Mathematics categories.
Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Topics include one-dimensional wave equation, properties of elliptic and parabolic equations, separation of variables and Fourier series, nonhomogeneous problems, and analytic functions of a complex variable. Solutions. 1965 edition.
Seminar On Complex Multiplication
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Author : A. Borel
language : en
Publisher: Springer
Release Date : 2007-08-16
Seminar On Complex Multiplication written by A. Borel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-16 with Mathematics categories.
Class Field Theory
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Author : Georges Gras
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Class Field Theory written by Georges Gras and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
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.
Recent Developments In Conformal Field Theories Trieste Conference
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Author : Seifallah Randjbar-daemi
language : en
Publisher: World Scientific
Release Date : 1990-06-27
Recent Developments In Conformal Field Theories Trieste Conference written by Seifallah Randjbar-daemi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-06-27 with categories.
Primes Of The Form X2 Ny2 Fermat Class Field Theory And Complex Multiplication Third Edition With Solutions
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Author : David A. Cox
language : en
Publisher: American Mathematical Soc.
Release Date : 2022-11-16
Primes Of The Form X2 Ny2 Fermat Class Field Theory And Complex Multiplication Third Edition With Solutions written by David A. Cox and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-16 with Education categories.
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.
About Vectors
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Author : Banesh Hoffmann
language : en
Publisher: Courier Corporation
Release Date : 2012-05-24
About Vectors written by Banesh Hoffmann and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.
From his unusual beginning in "Defining a vector" to his final comments on "What then is a vector?" author Banesh Hoffmann has written a book that is provocative and unconventional. In his emphasis on the unresolved issue of defining a vector, Hoffmann mixes pure and applied mathematics without using calculus. The result is a treatment that can serve as a supplement and corrective to textbooks, as well as collateral reading in all courses that deal with vectors. Major topics include vectors and the parallelogram law; algebraic notation and basic ideas; vector algebra; scalars and scalar products; vector products and quotients of vectors; and tensors. The author writes with a fresh, challenging style, making all complex concepts readily understandable. Nearly 400 exercises appear throughout the text. Professor of Mathematics at Queens College at the City University of New York, Banesh Hoffmann is also the author of The Strange Story of the Quantum and other important books. This volume provides much that is new for both students and their instructors, and it will certainly generate debate and discussion in the classroom.
High Primes And Misdemeanours Lectures In Honour Of The 60th Birthday Of Hugh Cowie Williams
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Author : A. J. Van Der Poorten
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
High Primes And Misdemeanours Lectures In Honour Of The 60th Birthday Of Hugh Cowie Williams written by A. J. Van Der Poorten and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.