Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The ratio and generating function of cogrowth coefficients of finitely
  generated groups   Let G be a group generated by $r$ elements $g_1,g_2,..., g_r.$ Among the
reduced words in $g_1,g_2,..., g_r$ of length $n$ some, say $\gamma_n,$
represent the identity element of the group $G.$ It has been shown in a
combinatorial way that the $2n$th root of $\gamma_{2n}$ has a limit, called the
cogrowth exponent with respect to generators $g_1,g_2,..., g_r.$ We show by
analytic methods that the numbers $\gamma_n$ vary regularly; i.e. the ratio
$\gamma_{2n+2}/\gamma_{2n}$ is also convergent. Moreover we derive new precise
information on the domain of holomorphy of $\gamma(z),$ the generating function
associated with the coefficients $\gamma_n.$

16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin