Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Burgess bounds for multi-dimensional short mixed character sums   This paper proves Burgess bounds for short mixed character sums in
multi-dimensional settings. The mixed character sums we consider involve both
an exponential evaluated at a real-valued multivariate polynomial, and a
product of multiplicative Dirichlet characters. We combine a multi-dimensional
Burgess method with recent results on multi-dimensional Vinogradov Mean Value
Theorems for translation-dilation invariant systems in order to prove character
sum bounds in any dimension that recapture the Burgess bound in dimension 1.
Moreover, we show that by embedding the given polynomial into an advantageously
chosen translation-dilation invariant system constructed in terms of that
polynomial, we may in many cases significantly improve the bound for the
associated character sum, due to a novel phenomenon that occurs only in
dimensions two and higher.

33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys