An Introduction To Algebraic Number Theory
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Algebraic Number Theory
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Author : Jürgen Neukirch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Algebraic Number Theory written by Jürgen Neukirch 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 2013-03-14 with Mathematics categories.
From the review: "The present book has as its aim to resolve a discrepancy in the textbook literature and ... to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (one-dimensional) arithmetic algebraic geometry. ... Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner... The author discusses the classical concepts from the viewpoint of Arakelov theory.... The treatment of class field theory is ... particularly rich in illustrating complements, hints for further study, and concrete examples.... The concluding chapter VII on zeta-functions and L-series is another outstanding advantage of the present textbook.... The book is, without any doubt, the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available." W. Kleinert in: Zentralblatt für Mathematik, 1992
An Introduction To Algebraic Number Theory
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Author : Takashi Ono
language : en
Publisher:
Release Date : 2014-09-01
An Introduction To Algebraic Number Theory written by Takashi Ono and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
An Introduction To Algebraic Number Theory
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Author : Takashi Ono
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Introduction To Algebraic Number Theory written by Takashi Ono 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 2012-12-06 with Mathematics categories.
This book is a translation of my book Suron Josetsu (An Introduction to Number Theory), Second Edition, published by Shokabo, Tokyo, in 1988. The translation is faithful to the original globally but, taking advantage of my being the translator of my own book, I felt completely free to reform or deform the original locally everywhere. When I sent T. Tamagawa a copy of the First Edition of the original work two years ago, he immediately pointed out that I had skipped the discussion of the class numbers of real quadratic fields in terms of continued fractions and (in a letter dated 2/15/87) sketched his idea of treating continued fractions without writing explicitly continued fractions, an approach he had first presented in his number theory lectures at Yale some years ago. Although I did not follow his approach exactly, I added to this translation a section (Section 4. 9), which nevertheless fills the gap pointed out by Tamagawa. With this addition, the present book covers at least T. Takagi's Shoto Seisuron Kogi (Lectures on Elementary Number Theory), First Edition (Kyoritsu, 1931), which, in turn, covered at least Dirichlet's Vorlesungen. It is customary to assume basic concepts of algebra (up to, say, Galois theory) in writing a textbook of algebraic number theory. But I feel a little strange if I assume Galois theory and prove Gauss quadratic reciprocity.
Introduction To Algebraic Number Theory
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Author : Henry Berthold Mann
language : en
Publisher:
Release Date : 1955
Introduction To Algebraic Number Theory written by Henry Berthold Mann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1955 with Algebraic number theory categories.
A Conversational Introduction To Algebraic Number Theory
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Author : Paul Pollack
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-01
A Conversational Introduction To Algebraic Number Theory written by Paul Pollack 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 2017-08-01 with Mathematics categories.
Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.
Algebraic Number Theory
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Author : Edwin Weiss
language : en
Publisher: Courier Corporation
Release Date : 2012-01-27
Algebraic Number Theory written by Edwin Weiss and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-27 with Mathematics categories.
Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.
A Brief Introduction To Algebraic Number Theory
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Author : J. S. Chahal
language : en
Publisher:
Release Date : 2003
A Brief Introduction To Algebraic Number Theory written by J. S. Chahal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Algebraic Number Theory
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Author : Zhang Xian Ke
language : en
Publisher: ALPHA SCIENCE INTERNATIONAL LIMITED
Release Date : 2016-03-14
Algebraic Number Theory written by Zhang Xian Ke and has been published by ALPHA SCIENCE INTERNATIONAL LIMITED this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-14 with Mathematics categories.
ALGEBRAIC NUMBER THEORY provides concisely both the fundamental and profound theory, starting from the succinct ideal theory (Chapters 1-3), turning then to valuation theory and local completion field (Chapters 4-5) which is the base of modern approach. After specific discussions on class numbers, units, quadratic and cyclotomic fields, and analytical theory (Chapters 6-8), the important Class Field Theory (Chapter 9) is expounded, and algebraic function field (Chapter 10) is sketched. This book is based on the study and lectures of the author at several universities.
Algebraic Number Theory
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Author : H. Koch
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-09-12
Algebraic Number Theory written by H. Koch 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 1997-09-12 with Mathematics categories.
From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Koch's book is written mostly for non-specialists. It is an up-to-date account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians." Acta Scientiarum Mathematicarum, 1993
Algebraic Number Theory
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Algebraic Number Theory written by Serge Lang 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 present book gives an exposition of the classical basic algebraic and analytic number theory and supersedes my Algebraic Numbers, including much more material, e. g. the class field theory on which 1 make further comments at the appropriate place later. For different points of view, the reader is encouraged to read the collec tion of papers from the Brighton Symposium (edited by Cassels-Frohlich), the Artin-Tate notes on class field theory, Weil's book on Basic Number Theory, Borevich-Shafarevich's Number Theory, and also older books like those of W eber, Hasse, Hecke, and Hilbert's Zahlbericht. It seems that over the years, everything that has been done has proved useful, theo retically or as examples, for the further development of the theory. Old, and seemingly isolated special cases have continuously acquired renewed significance, often after half a century or more. The point of view taken here is principally global, and we deal with local fields only incidentally. For a more complete treatment of these, cf. Serre's book Corps Locaux. There is much to be said for a direct global approach to number fields. Stylistically, 1 have intermingled the ideal and idelic approaches without prejudice for either. 1 also include two proofs of the functional equation for the zeta function, to acquaint the reader with different techniques (in some sense equivalent, but in another sense, suggestive of very different moods).