Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Problems and Results related to Waring's problem: Maximal functions and
  ergodic averages   We study the arithmetic analogue of maximal functions on diagonal
hypersurfaces. This paper is a natural step following the papers of
\cite{Magyar_dyadic}, \cite{Magyar_ergodic} and \cite{MSW}. We combine more
precise knowledge of oscillatory integrals and exponential sums to generalize
the asymptotic formula in Waring's problem to an approximation formula for the
fourier transform of the solution set of lattice points on hypersurfaces
arising in Waring's problem and apply this result to arithmetic maximal
functions and ergodic averages. In sufficiently large dimensions, the
approximation formula, $\ell^2$-maximal theorems and ergodic theorems were
previously known. Our contribution is in reducing the dimensional constraint in
the approximation formula using recent bounds of Wooley, and improving the
range of $\ell^p$ spaces in the maximal and ergodic theorems. We also
conjecture the expected range of spaces.

17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org