Springer Monographs in Mathematics

Arithmetic of Quadratic Forms

Authors: Shimura, Goro

  • Examines algebraic number theory and the theory of semisimple algebras
  • Covers classification over an algebraic number field and classification over the ring of algebraic integers
  • Discusses local class field theory
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eBook $119.00
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  • ISBN 978-1-4419-1732-4
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Hardcover $159.00
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  • ISBN 978-1-4419-1731-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-1-4614-2618-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

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)


Table of contents (7 chapters)

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-1-4419-1732-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-1-4419-1731-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-1-4614-2618-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Arithmetic of Quadratic Forms
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2010
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4419-1732-4
DOI
10.1007/978-1-4419-1732-4
Hardcover ISBN
978-1-4419-1731-7
Softcover ISBN
978-1-4614-2618-9
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XII, 238
Topics