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Matematicheskie Zametki, 2016, Volume 99, Issue 4, Pages 603–612
DOI: https://doi.org/10.4213/mzm10858 (Mi mzm10858) 		 
Trigonometric Integrals over One-Dimensional Quasilattices of Arbitrary Codimension

A. V. Shutov

Vladimir State University
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DOI: https://doi.org/10.4213/mzm10858
Abstract: The class of one-dimensional quasilattices parametrized by translations of the torus is studied. The trigonometric integrals averaging the moduli of trigonometric sums related to quasilattices are considered for this class. Nontrivial estimates of such integrals are obtained. The relationship between trigonometric integrals and several problems in the theory of Diophantine approximations is discussed.
Keywords: quasilattice, parametrization by translations, trigonometric integral, trigonometric sum, codimension, exchanged tiling of the torus, Diophantine approximation, Weyl's uniform distribution theorem.
Funding agency Grant number
Russian Science Foundation 14-11-00433
This work was supported by the Russian Science Foundation under grant 14-11-00433.
Received: 03.08.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 4, Pages 590–597
DOI: https://doi.org/10.1134/S0001434616030329
Bibliographic databases:
Document Type: Article
UDC: 511.3
Language: Russian
Citation: A. V. Shutov, “Trigonometric Integrals over One-Dimensional Quasilattices of Arbitrary Codimension”, Mat. Zametki, 99:4 (2016), 603–612; Math. Notes, 99:4 (2016), 590–597
Citation in format AMSBIB
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