An Introduction to the Geometry of Numbers

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Springer Science & Business Media, 6 déc. 2012 - 345 pages
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From the reviews: "The work is carefully written. It is well motivated, and interesting to read, even if it is not always easy... historical material is included... the author has written excellent account of an interesting subject." Mathematical Gazette "A well-written, very thorough account ... Among the topi are lattices, reduction, Minkowskis Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references." The American Mathematical Monthly
 

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Table des matières

Lattices
9
Reduction
26
Representation of integers by quadratic forms
99
MAHLERs compactness theorem
121
The theorem of MINKowskiHLAwKA
175
The quotient space
194
Successive minima
201
Packings
223
Automorphs
256
Inhomogeneous problems
303
Appendix
332
Index
343
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À propos de l'auteur (2012)

Biography of J.W.S. Cassels

J. W. S. Cassels (known to his friends by the Gaelic form "Ian" of his first name) was born of mixed English-Scottish parentage on 11 July 1922 in the picturesque cathedral city of Durham. With a first degree from Edinburgh, he commenced research in Cambridge in 1946 under L. J. Mordell, who had just succeeded G. H. Hardy in the Sadleirian Chair of Pure Mathematics. He obtained his doctorate and was elected a Fellow of Trinity College in 1949. After a year in Manchester, he returned to Cambridge and in 1967 became Sadleirian Professor. He was Head of the Department of Pure Mathematics and Mathematical Statistics from 1969 until he retired in 1984.

Cassels has contributed to several areas of number theory and written a number of other expository books:
- An introduction to diophantine approximations
- Rational quadratic forms
- Economics for mathematicians
- Local fields
- Lectures on elliptic curves
- Prolegomena to a middlebrow arithmetic of curves of genus 2 (with E. V. Flynn).

Informations bibliographiques