Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating the main conjecture in Vinogradov's mean value theorem   We apply multigrade efficient congruencing to estimate Vinogradov's integral
of degree $k$ for moments of order $2s$, establishing strongly diagonal
behaviour for $1\le s\le \frac{1}{2}k(k+1)-\frac{1}{3}k+o(k)$. In particular,
as $k\rightarrow \infty$, we confirm the main conjecture in Vinogradov's mean
value theorem for 100% of the critical interval $1\le s\le \frac{1}{2}k(k+1)$.

37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg