Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partial Factorizations of Products of Binomial Coefficients   Let $G_n= \prod_{k=0}^n \binom{n}{k},$ the product of the elements of the
$n$-th row of Pascal's triangle. This paper studies the partial factorizations
of $G_n$ given by the product $G(n,x)$ of all prime factors $p$ of $G_n$ having
$p \le x$, counted with multiplicity. It shows $\log G(n, \alpha n) \sim
f_G(\alpha)n^2$ as $n \to \infty$ for a limit function $f_{G}(\alpha)$ defined
for $0 \le \alpha \le 1$. The main results are deduced from study of functions
$A(n, x), B(n,x),$ that encode statistics of the base $p$ radix expansions of
the integer $n$ (and smaller integers), where the base $p$ ranges over primes
$p \le x$. Asymptotics of $A(n,x)$ and $B(n,x)$ are derived using the prime
number theorem with remainder term or conditionally on the Riemann hypothesis.

18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
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
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an