An Introduction to the Geometry of Numbers

Couverture
Springer Science & Business Media, 16 déc. 1996 - 345 pages
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
 

Pages sélectionnées

Table des matières

II
1
III
9
IV
19
V
20
VI
23
VII
26
VIII
27
IX
30
XXXVII
184
XXXVIII
187
XXXIX
189
XL
194
XLI
198
XLII
201
XLIII
205
XLIV
207

X
35
XI
51
XII
60
XIII
64
XIV
68
XV
73
XVI
78
XVII
80
XVIII
84
XIX
98
XX
103
XXI
105
XXII
108
XXIII
119
XXIV
121
XXV
122
XXVI
126
XXVII
134
XXVIII
141
XXIX
145
XXX
152
XXXI
155
XXXII
163
XXXIII
165
XXXIV
175
XXXV
178
XXXVI
181
XLV
213
XLVI
219
XLVII
223
XLIX
228
L
231
LI
235
LII
240
LIII
245
LIV
246
LV
250
LVI
256
LVII
266
LVIII
268
LIX
279
LX
286
LXI
295
LXII
298
LXIII
301
LXIV
303
LXV
309
LXVI
313
LXVII
322
LXVIII
332
LXIX
334
LXX
343
Droits d'auteur

Autres éditions - Tout afficher

An Introduction to the Geometry of Numbers
John William Scott Cassels
Affichage d'extraits - 1971
An Introduction to the Geometry of Numbers
J W S (John William Scott) Cassels
Aucun aperçu disponible - 2021
An Introduction to the Geometry of Numbers
J W S (John William Scott) Cassels
Aucun aperçu disponible - 2021

Expressions et termes fréquents

a₁ a₂ admissible lattices arbitrarily small automorph b₁ b₂ basis for Ʌ boundary point bounded bounded set c₁ CASSELS Chapter clearly co-ordinates concludes the proof convex body theorem convex set convex symmetric Corollary critical lattice DAVENPORT defined definite quadratic form denote determinant distance function exist finite number Geometry of Numbers given Hence homogeneous linear transformation inequality infimum infinitely integers K₁ lattice constant lattice Ʌ Lemma Let b₁ Let F(x Let Ʌ linear transformation linearly independent linearly independent points M₁ MAHLER Minkowski-Hlawka Theorem MINKOWSKI'S convex body MINKOWSKI's theorem n-dimensional N₁ parallelopiped points of Ʌ proof of Theorem quadratic form quotient space real numbers result ROGERS S-admissible satisfies sequence set of points shape star-body successive minima suppose without loss symmetric convex tac-plane Theorem II Theorem VII u₁ u₂ v₁ vectors x₁ Y₁ α₁ ΕΛ

Références à ce livre

À propos de l'auteur (1996)

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

TitreAn Introduction to the Geometry of Numbers
Classics in Mathematics
AuteurJ.W.S. Cassels
Éditionillustrée, réimprimée
ÉditeurSpringer Science & Business Media, 1996
ISBN3540617884, 9783540617884
Longueur345 pages
  
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