The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere

被引：60
作者：
Brauchart, J. S. [1 ]
Hardin, D. P. [2 ]
Saff, E. B. [2 ]
机构：
[1] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia
[2] Vanderbilt Univ, Dept Math, Ctr Construct Approximat, Nashville, TN 37240 USA
来源：
RECENT ADVANCES IN ORTHOGONAL POLYNOMIALS, SPECIAL FUNCTIONS, AND THEIR APPLICATIONS | 2011年 / 578卷
基金：
美国国家科学基金会;
关键词：
Dirichlet function; Logarithmic Energy; Riemann Zeta function; Riesz energy; MINIMAL DISCRETE ENERGY; POINTS; DISTANCES; SUMS; CONFIGURATIONS; SURFACE; BOUNDS;
D O I：
10.1090/conm/578/11483
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We survey known results and present estimates and conjectures for the next-order term in the asymptotics of the optimal logarithmic energy and Riesz s-energy of N points on the unit sphere in Rd+1, d >= 1. The conjectures are based on analytic continuation assumptions (with respect to s) for the coefficients in the asymptotic expansion (as N -> infinity) of the optimal s-energy.
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页码：31 / +
页数：4
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