Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Erd\H{o}s-Sur\'anyi sequences and trigonometric integrals   We study representations of integers as sums of the form $\pm a_1\pm a_2\pm
\dotsb \pm a_n$, where $a_1,a_2,\ldots$ is a prescribed sequence of integers.
Such a sequence is called an Erd\H{o}s-Sur\'anyi sequence if every integer can
be written in this form for some $n\in\mathbb{N}$ and choices of signs in
infinitely many ways. We study the number of representations of a fixed
integer, which can be written as a trigonometric integral, and obtain an
asymptotic formula under a rather general scheme due to Roth and Szekeres. Our
approach, which is based on Laplace's method for approximating integrals, can
also be easily extended to find higher-order expansions. As a corollary, we
settle a conjecture of Andrica and Iona\c{s}cu on the number of solutions to
the signum equation $\pm 1^k \pm 2^k \pm \dotsb \pm n^k = 0$.

9
The categories of this paper are: nlin
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys