Authors:
- 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
Part of the book series: Springer Monographs in Mathematics (SMM)
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (7 chapters)
-
Front Matter
-
Back Matter
About this book
Reviews
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)
Authors and Affiliations
-
Department of Mathematics, Princeton University, Princeton, USA
Goro Shimura
Bibliographic Information
Book Title: Arithmetic of Quadratic Forms
Authors: Goro Shimura
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-1-4419-1732-4
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2010
Hardcover ISBN: 978-1-4419-1731-7Published: 30 June 2010
Softcover ISBN: 978-1-4614-2618-9Published: 05 September 2012
eBook ISBN: 978-1-4419-1732-4Published: 09 August 2010
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XII, 238
Topics: Number Theory, Algebra, General Algebraic Systems