Arithmetic of Quadratic Forms: Springer Monographs in Mathematics
Autor Goro Shimuraen Limba Engleză Paperback – 5 sep 2012
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Paperback (1) | 1072.71 lei 6-8 săpt. | |
Springer – 5 sep 2012 | 1072.71 lei 6-8 săpt. | |
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Springer – 30 iun 2010 | 1079.90 lei 6-8 săpt. |
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Specificații
ISBN-13: 9781461426189
ISBN-10: 1461426189
Pagini: 252
Ilustrații: XII, 238 p.
Dimensiuni: 155 x 235 x 13 mm
Greutate: 0.32 kg
Ediția:2010
Editura: Springer
Colecția Springer
Seria Springer Monographs in Mathematics
Locul publicării:New York, NY, United States
ISBN-10: 1461426189
Pagini: 252
Ilustrații: XII, 238 p.
Dimensiuni: 155 x 235 x 13 mm
Greutate: 0.32 kg
Ediția:2010
Editura: Springer
Colecția Springer
Seria Springer Monographs in Mathematics
Locul publicării:New York, NY, United States
Public țintă
ResearchCuprins
The Quadratic Reciprocity Law.- Arithmetic in an Algebraic Number Field.- Various Basic Theorems.- Algebras Over a Field.- Quadratic Forms.- Deeper Arithmetic of Quadratic Forms.- Quadratic Diophantine Equations.
Recenzii
From the reviews:
“This impressive monograph is devoted to some aspects of the arithmetic theory of quadratic forms to which the author has made important contributions in recent years. … Anyone with an interest in the book’s topic will find this volume well worth his or her time.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 169 (1), January, 2013)
“In this book Goro Shimura presents some very interesting material in a clear and readable style. … There is plenty to learn from an introduction to a highly technical subject by one of its leaders. … The book will serve well as a basis for a couple of postgraduate courses. … the material is essentially self-contained the exposition is often very technical … .” (Peter Shiu, The Mathematical Gazette, Vol. 96 (536), July, 2012)
“Beginners and experts … have much to gain from the author’s insights and perspectives presented in this book on the arithmetic theory of quadratic forms. … In order to make the treatment of these topics accessible to readers with a general background in abstract algebra, the author includes preliminary material on algebraic number theory and the theory of semisimple algebras. Throughout the book, the presentation is concise and elegant.” (A. G. Earnest, Mathematical Reviews, Issue 2011 m)
“Goro Shimura is one of the world’s premier arithmeticians, with his name attached to a number of marvelous things. … it presents a lot more than its title suggests and does so magnificently. … Shimura’s Arithmetic of Quadratic Forms is another very important monograph by this fine scholar and, to use a hackneyed but apt phrase, will richly repay the reader who invests his time in a careful study of its pages.” (Michael Berg, The Mathematical Association of America, August, 2010)
“This impressive monograph is devoted to some aspects of the arithmetic theory of quadratic forms to which the author has made important contributions in recent years. … Anyone with an interest in the book’s topic will find this volume well worth his or her time.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 169 (1), January, 2013)
“In this book Goro Shimura presents some very interesting material in a clear and readable style. … There is plenty to learn from an introduction to a highly technical subject by one of its leaders. … The book will serve well as a basis for a couple of postgraduate courses. … the material is essentially self-contained the exposition is often very technical … .” (Peter Shiu, The Mathematical Gazette, Vol. 96 (536), July, 2012)
“Beginners and experts … have much to gain from the author’s insights and perspectives presented in this book on the arithmetic theory of quadratic forms. … In order to make the treatment of these topics accessible to readers with a general background in abstract algebra, the author includes preliminary material on algebraic number theory and the theory of semisimple algebras. Throughout the book, the presentation is concise and elegant.” (A. G. Earnest, Mathematical Reviews, Issue 2011 m)
“Goro Shimura is one of the world’s premier arithmeticians, with his name attached to a number of marvelous things. … it presents a lot more than its title suggests and does so magnificently. … Shimura’s Arithmetic of Quadratic Forms is another very important monograph by this fine scholar and, to use a hackneyed but apt phrase, will richly repay the reader who invests his time in a careful study of its pages.” (Michael Berg, The Mathematical Association of America, August, 2010)
Textul de pe ultima copertă
This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case.To make the book concise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are stated with an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references.
Caracteristici
Discusses algebraic number theory and the theory of semisimple algebras Discusses classification of quadratic forms over the ring of algebraic integers Discusses local class field theory Presents a new framework of quadratic Diophantine equations Includes supplementary material: sn.pub/extras