Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete Energy Asymptotics on a Riemannian circle   We derive the complete asymptotic expansion in terms of powers of $N$ for the
geodesic $f$-energy of $N$ equally spaced points on a rectifiable simple closed
curve $\Gamma$ in ${\mathbb R}^p$, $p\geq2$, as $N \to \infty$. For $f$
decreasing and convex, such a point configuration minimizes the $f$-energy
$\sum_{j\neq k}f(d(\mathbf{x}_j, \mathbf{x}_k))$, where $d$ is the geodesic
distance (with respect to $\Gamma$) between points on $\Gamma$. Completely
monotonic functions, analytic kernel functions, Laurent series, and weighted
kernel functions $f$ are studied. % Of particular interest are the geodesic
Riesz potential $1/d^s$ ($s \neq 0$) and the geodesic logarithmic potential
$\log(1/d)$. By analytic continuation we deduce the expansion for all complex
values of $s$.

21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga