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Matematicheskie Zametki, 2015, Volume 97, Issue 5, Pages 781–793
DOI: https://doi.org/10.4213/mzm10655 (Mi mzm10655) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Trigonometric Sums over One-Dimensional Quasilattices of Arbitrary Codimension

A. V. Shutov

Vladimir State University
Full-text PDF (518 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm10655
Abstract: A new class of one-dimensional quasilattices parametrized by the translations of the torus is introduced. For this class, parameter-dependent trigonometric sums over points of quasilattice are considered. Nontrivial estimates of the trigonometric sums under consideration are obtained. For a number of trigonometric sums of special form, asymptotic formulas are derived. It is proved that the distribution of points of quasilattices is uniform modulo $h$ for almost all $h$. Earlier similar results were obtained in the particular case of quasilattices parametrized by the rotations of the circle.
Keywords: trigonometric sum, quasilattice, codimension, bounded remainder set, tiling of the torus, Weyl's uniform distribution theorem, averaged lattice value, Koksma–Hlawka inequality, orbit structure.
Funding agency Grant number
Russian Science Foundation 14-11-00433
This work was supported by the Russian Science Foundation (grant no. 14-11-00433).
Received: 31.07.2014
English version:
Mathematical Notes, 2015, Volume 97, Issue 5, Pages 791–802
DOI: https://doi.org/10.1134/S0001434615050144
Bibliographic databases:
Document Type: Article
UDC: 511.3
Language: Russian
Citation: A. V. Shutov, “Trigonometric Sums over One-Dimensional Quasilattices of Arbitrary Codimension”, Mat. Zametki, 97:5 (2015), 781–793; Math. Notes, 97:5 (2015), 791–802
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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