Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The asymptotic expansion of a sum appearing in an approximate functional
  equation for the riemann zeta function   A representation for the Riemann zeta function valid for arbitrary complex
$s=\sigma+it$ is $\zeta(s)=\sum_{n=0}^\infty A(n,s)$, where
  \[A(n,s)=\frac{2^{-n-1}}{1-2^{1-s}} \sum_{k=0}^n
\left(\!\begin{array}{c}n\\k\end{array}\!\right) \frac{(-)^k}{(k+1)^s}.\] In
this note we examine the asymptotics of $A(n,s)$ as $n\to\infty$ when $t=an$,
where $a>0$ is a fixed parameter, by application of the method of steepest
descents to an integral representation. Numerical results are presented to
illustrate the accuracy of the expansion obtained.

32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol