Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Double exponential sums and congruences with intervals and exponential
  functions modulo a prime   Let $p$ be a large prime number and $g$ be any integer of multiplicative
order $T$ modulo $p$. We obtain a new estimate of the double exponential sum $$
S=\sum_{n\in \mathcal{N}}\left|\sum_{m\in \mathcal{M} }e_p(an g^{m})\right|,
\quad \gcd (a,p)=1, $$ where $\mathcal{N}$ and $\mathcal{M}$ are intervals of
consecutive integers with $|\mathcal{N}|=N$ and $|\mathcal{M}|=M<T$ elements.
One representative example is the following consequence of the main result: if
$N=M\approx p^{1/3}$, then $|S|< N^{2-1/8 + o(1)}$. We then apply our estimate
to obtain new results on additive congruences involving intervals and
exponential functions.

10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
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The categories of this paper are: econ
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol