Ergodic Properties of Algebraic Fields (Paperback, Softcover reprint of the original 1st ed. 1968)

The applications of ergodic theory to metric number theory are well known; part of the latter theory turns out to be essentially a special case of general ergodic theorems. In the present book other applications of ergodic concepts are presented. Constructing "flows" of integral points on certain algebraic manifolds given by systems of integral polynomials, we are able to prove individual ergodic theorems and mixing theorems in certain cases. These theorems permit asymptotic calculations of the distributions of integral points on such manifolds, and we arrive at results inaccessible up to now by the usual methods of analytic number theory. Typical in this respect is the theorem concerning the asymptotic distribution and ergodic behavior of the set of integral points on the sphere X2+ y2+z2=m for increasing m. It is not known up until now how to obtain the simple and geometrically obvious regularity of the distribution of integral points on the sphere other than by ergodic methods. Systems of diophantine equations are studied with our method, and flows of integral points introduced for this purpose turn out to be closely connected with the behavior of ideal classes of the corresponding algebraic fields, and this behavior shows certain ergodic regularity in sequences of algebraic fields. However, in this book we examine in this respect only quadratic fields in sufficient detail, studying fields of higher degrees only in chapter VII.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, 45
Release date:	April 2012
First published:	1968
Translators:	M.S. Keane
Authors:	Yurij V Linnik
Dimensions:	235 x 155 x 11mm (L x W x T)
Format:	Paperback
Pages:	194
Edition:	Softcover reprint of the original 1st ed. 1968
ISBN-13:	978-3-642-86633-3
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Number theory > General Books > Science & Mathematics > Mathematics > Applied mathematics > Non-linear science
LSN:	3-642-86633-6
Barcode:	9783642866333

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