Generalized continued fractions and ergodic theory
type: Item
instance of: scholarly article
title: Generalized continued fractions and ergodic theory
zbMATH Open document ID: 0982.11038
DOI: 10.1007/BF02169055
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-12-12T00:00:00Z
review text: The author constructs a new theory of generalized continued fractions, \((A,\omega)\)-continued fractions, for vectors \(\omega=(\omega_1,\dots,\omega_n)\) with \(0\leq\omega_s<1\) (\(s=1,\dots,n\)) and some map \(A\) of real \(n\)-dimensional space. This theory is applied to solve some problems of analysis and number theory: finding the estimates of Weyl sums and the remainder terms in the laws of distribution and joint distribution of fractional parts of the values of polynomials.
reviewed by: Takao Komatsu
Mathematics Subject Classification ID: 11J70
Mathematics Subject Classification ID: 37A45
Mathematics Subject Classification ID: 11J54
Mathematics Subject Classification ID: 11L15
zbMATH DE Number: 1376343
zbMATH Keywords: continued fractions
zbMATH Keywords: ergodic theory
zbMATH Keywords: Weyl sums
author: L. D. Pustyl'nikov
MaRDI profile type: Publication
cites work: Q5560061
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description: scientific article; zbMATH DE number 1376343