Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A glimpse inside the mathematical kitchen   We prove the inequality sum_{k=1}^infty (-1)^{k+1} r^k cos(k*phi) (k+2)^{-1}
< sum_{k=1}^infty(-1)^{k+1} r^k (k+2)^{-1} for 0 < r <= 1 and 0 < phi < pi. For
the case r = 1 we give two proofs. The first one is by means of a general
numerical technique (maximal slope principle) for proving inequalities between
elementary functions. The second proof is fully analytical. Finally we prove a
general rearrangement theorem and apply it to the remaining case 0 < r < 1.
Some of these inequalities are needed for obtaining general sharp bounds for
the errors committed when applying the Riemann-Siegel expansion of Riemann's
zeta function.

24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom