Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equidistribution and inequalities for partitions into powers   If $ p_k(a,m,n) $ denotes the number of partitions of $n$ into $k$th powers
with a number of parts that is congruent to $ a $ modulo $m,$ then
$p_2(0,2,n)\sim p_2(1,2,n)$ and the sign of the difference $p_2(0,2,n)-
p_k(1,2,n)$ alternates with the parity of $n,$ as proven by recent work of the
author (2020). In this paper, we place the problem in a broader framework. By
analytic arguments using the circle method and Gauss sums estimates, we show
that the same results hold for any $ k\ge2. $ By combinatorial arguments, we
show that the sign of the difference $p_k(0,2,n)- p_k(1,2,n)$ depends on the
parity of $n$ for a larger class of partitions.

31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th