On lattice sums and Wigner limits

DOI10.1016/j.jmaa.2014.01.008zbMath1369.11046arXiv1310.1423OpenAlexW2963898918MaRDI QIDQ2338774

Armin Straub, David Borwein, Jonathan M. Borwein

Publication date: 27 March 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.1423

zbMATH Keywords

analytic continuationlattice sumsWigner electron sums

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Lattices and convex bodies (number-theoretic aspects) (11H06) Trigonometric and exponential sums (general theory) (11L03)

Related Items (8)

Coulomb and Riesz gases: The known and the unknown ⋮ Statistical mechanics of the uniform electron gas ⋮ A Unified Trapezoidal Quadrature Method for Singular and Hypersingular Boundary Integral Operators on Curved Surfaces ⋮ Generation of off-critical zeros for hypercubic Epstein zeta functions ⋮ Floating Wigner crystal and periodic jellium configurations ⋮ Corrected trapezoidal rules for boundary integral equations in three dimensions ⋮ High-precision arithmetic in mathematical physics ⋮ Uniform bounds for lattice point counting and partial sums of zeta functions

Uses Software

• DLMF

Cites Work

• On Dirichlet series for sums of squares
• Analysis of certain lattice sums
• Über Gitterpunkte in vierdimensionalen Ellipsoiden. (On lattice points in four-dimensional ellipsoids)
• The vanishing of Ramanujan's function \(\tau(n)\)
• Energy of static electron lattices
• Exponential Sums and Lattice Points III
• Lattice Sums Then and Now
• A Lattice-Point Problem. II
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