Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generic Newton polygon for exponential sums in $n$ variables with
  parallelotope base   Let $p$ be a prime number. Every $n$-variable polynomial $f(\underline x)$
over a finite field of characteristic $p$ defines an Artin--Schreier--Witt
tower of varieties whose Galois group is isomorphic to $\mathbb{Z}_p$. Our goal
of this paper is to study the Newton polygon of the $L$-function associated to
a finite character of $\mathbb{Z}_p$ and a generic polynomial whose convex hull
is an $n$-dimensional paralleltope $\Delta$. We denote this polygon by
$\mathrm{GNP}(\Delta)$. We prove a lower bound of $\mathrm{GNP}(\Delta)$, which
is called the improved Hodge polygon $\mathrm{IHP}(\Delta)$. We show that
$\mathrm{IHP}(\Delta)$ lies above the usual Hodge polygon $\mathrm{HP}(\Delta)$
at certain infinitely many points, and when $p$ is larger than a fixed number
determined by $\Delta$, it coincides with $\mathrm{GNP}(\Delta)$ at these
points. As a corollary, we roughly determine the distribution of the slopes of
$\mathrm{GNP}(\Delta)$.

10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess