Next order energy asymptotics for Riesz potentials on flat tori

2015/11/04 by Douglas P. Hardin, Edward B. Saff, Hardin, Douglas P. +5 · 2 citations
Mathematics · Computer Science · #Mathematical Approximation and Integration #Spectral Theory in Mathematical Physics #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1511.01552

Abstract

Let Λ be a lattice in \bf R^d with positive co-volume. Among Λ-periodic N-point configurations, we consider the minimal renormalized Riesz s-energy E_s,Λ(N). While the dominant term in the asymptotic expansion of E_s,Λ(N) as N goes to infinity in the long range case that 00 they are of the form C_s,d|Λ|^-s/dN^1+s/d and -(2)/(d)Nlog N+(C_log,d-2ζ'_Λ(0))N where we show that the constant C_s,d is independent of the lattice Λ.

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