Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An asymptotic expansion for the generalised quadratic Gauss sum
  revisited   An asymptotic expansion for the generalised quadratic Gauss sum
$$S_N(x,\theta)=\sum_{j=1}^{N} \exp (\pi ixj^2+2\pi ij\theta),$$ where $x$,
$\theta$ are real and $N$ is a positive integer, is obtained as $x\rightarrow
0$ and $N\rightarrow\infty$ such that $Nx$ is finite. The form of this
expansion holds for all values of $Nx+\theta$ and, in particular, in the
neighbourhood of integer values of $Nx+\theta$. A simple bound for the
remainder in the expansion is derived. Numerical results are presented to
demonstrate the accuracy of the expansion and the sharpness of the bound.

32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys