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.
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