Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the number of irrational odd zeta values   It is proved that, for all odd integer $s \geqslant s_0(\varepsilon)$, there
are at least $\big( c_0 - \varepsilon \big) \frac{s^{1/2}}{(\log s)^{1/2}} $
many irrational numbers among the following odd zeta values:
$\zeta(3),\zeta(5),\zeta(7),\cdots,\zeta(s)$. The constant $c_0 =
1.192507\ldots$ can be expressed in closed form. The work is based on the
previous work of Fischler, Sprang and Zudilin [FSZ19], improves the lower bound
$2^{(1-\varepsilon)\frac{\log s}{\log\log s}}$ therein. The main new ingredient
is an optimal design for the zeros of the auxiliary rational functions, which
relates to the inverse of Euler totient funtion.

11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol