109 citations · 567 across the 25 of their papers we have counts for
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Point sets on the sphere with small spherical cap discrepancy
Christoph Aistleitner, Johann Brauchart, Josef Dick
In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discre…
Explicit formulas for the Riesz energy of the th roots of unity
J. S. Brauchart
The paper Brauchart, Hardin and Saff [Bull. Lond. Math. Soc. 41(4) (2009)] gives the complete asymptotic expansions of the Riesz -energy of the th roots of unity which form a…
Optimal Discrete Riesz Energy and Discrepancy
J. S. Brauchart
The Riesz -energy of an -point configuration in the Euclidean space is defined as the sum of reciprocal -powers of all mutual distances in this system. In…
A Fascinating Polynomial Sequence arising from an Electrostatics Problem on the Sphere
J. S. Brauchart, P. D. Dragnev, E. B. Saff +1
A positive unit point charge approaching from infinity a perfectly spherical isolated conductor carrying a total charge of +1 will eventually cause a negatively charged spherical c…
A simple Proof of Stolarsky's Invariance Principle
Johann S. Brauchart, Josef Dick
Stolarsky [Proc. Amer. Math. Soc. 41 (1973), 575--582] showed a beautiful relation that balances the sums of distances of points on the unit sphere and their spherical cap $\mathbb…
Quasi-Monte Carlo rules for numerical integration over the unit sphere
Johann S. Brauchart, Josef Dick
We study numerical integration on the unit sphere using equal weight quadrature rules, where the weights are such that constant functions are in…