Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zeta function factorisation, Dwork hypersurfaces, hypergeometric
  hypersurfaces   Let $\mathbb{F}_q$ be a finite field with $q$ elements, $\psi$ a non-zero
element of $\mathbb{F}_q$, and $n$ an integer $\geq 3$ prime to $q$. The aim of
this article is to show that the zeta function of the projective variety over
$\mathbb{F}_q$ defined by $X_\psi \colon x_1^n+...+x_n^n - n \psi x_1... x_n=0$
has, when $n$ is prime and $X_\psi$ is non singular (i.e. when $\psi^n \neq
1$), an explicit decomposition in factors coming from affine varieties of odd
dimension $\leq n-4$ which are of hypergeometric type. The method we use
consists in counting separately the number of points of $X_\psi$ and of some
varieties of the preceding type and then compare them. This article answers, at
least when $n$ is prime, a question asked by D. Wan in his article "Mirror
Symmetry for Zeta Functions".

12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin