23 citations · 74 across the 30 of their papers we have counts for
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math-ph2020★ 3 cited
Electrostatic Equilibria on the Unit Circle via Jacobi Polynomials
Kev Johnson, Brian Simanek
We use classical Jacobi polynomials to identify the equilibrium configurations of charged particles confined to the unit circle. Our main result unifies two theorems from a 1986 pa…
math-ph2015★ 2 cited
Next order energy asymptotics for Riesz potentials on flat tori
Douglas P. Hardin, Edward B. Saff, Brian Z. Simanek +1
Let be a lattice in with positive co-volume. Among -periodic -point configurations, we consider the minimal renormalized Riesz -energy $\mathcal{E}_{s,Λ}(N…
math-ph2014★ 23 cited
Periodic Discrete Energy for Long-Range Potentials
D. P. Hardin, E. B. Saff, Brian Simanek
We consider periodic energy problems in Euclidean space with a special emphasis on long-range potentials that cannot be defined through the usual infinite sum. One of our main resu…