On a lattice point problem arising in the spectral analysis of periodic operators

DOI10.1112/S0025579300014819zbMath1101.11040OpenAlexW2097405639MaRDI QIDQ4676335

Alexander V. Sobolev, Sergei V. Konyagin, Maxim M. Skriganov

Publication date: 3 May 2005

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0025579300014819

zbMATH Keywords

lattice pointsspectrum of periodic operators

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Lattice points in specified regions (11P21)

Related Items (4)

A characterization theorem for the \(L^{2}\)-discrepancy of integer points in dilated polygons ⋮ On the spectrum of a limit-periodic Schrödinger operator ⋮ Deterministic and probabilistic discrepancies ⋮ Upper Bounds in Classical Discrepancy Theory

Cites Work

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• A remark on two dimensional periodic potentials
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• On the Bethe-Sommerfeld conjecture for the polyharmonic operator.
• Asymptotic of the density of states for the Schrödinger operator with periodic electric potential
• Minima of Cosine Sums and Maxima of Polynomials on the Unit Circle
• An estimate of the free term of a non-negative trigonometric polynomial with integer coefficients
• Lattice points, perturbation theory and the periodic polyharmonic operator.

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