Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Koksma-Hlawka-Potential Identity on the $d$ Dimensional Sphere and its
  Applications to Discrepancy   Let $d\geq 2$ be an integer, $S^d\subset {\mathbb R}^{d+1}$ the unit sphere
and $\sigma$ a finite signed measure whose positive and negative parts are
supported on $S^d$ with finite energy. In this paper, we derive an error
estimate for the quantity $\left|\int_{S^d}fd\sigma\right|$, for a class of
harmonic functions $f:\mathbb R^{d+1}\to \mathbb R$. Our error estimate
involves 2 sided bounds for a Newtonian potential with respect to $\sigma$ away
from its support. In particular, our main result allows us to study quadrature
errors, for scatterings on the sphere with given mesh norm.

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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga