论文标题
某些指数总和的L功能的HASSE多项式
Hasse Polynomials of L-functions of Certain Exponential Sums
论文作者
论文摘要
在本文中，我们专注于计算与以下laurent polyenmials y farmess相关的某些指数总和的较高坡度hasse多项式$ f（x_1，\ ldots，x_ {n+1}）= \ sum_ = \ sum_ = \ sum_ x_ {n+1} \ left（x_i+\ frac {1} {x_i} \ right）+a_ {n+1} x_ {n+1}+\ frac {1} {x__ {x_ {n+1}} $ n+1 $。我们找到了一个简单的公式，用于斜坡一侧的HASSE多项式，并研究这些Hasse多项式的不可约性。我们还将以$ n = 3 $的方式提供所有更高坡度的Hasse多项式的简单形式，回答了Zhang和Feng的开放问题。
In this paper, we focus on computing the higher slope Hasse polynomials of L-functions of certain exponential sums associated to the following family of Laurent polynomials $f(x_1,\ldots ,x_{n+1})=\sum_{i=1}^na_i x_{n+1}\left(x_i+\frac{1}{x_i}\right)+a_{n+1} x_{n+1}+\frac{1}{x_{n+1}}$, where $a_i \in \F^*_{q}$, $i=1,2, \ldots, n+1$. We find a simple formula for the Hasse polynomial of the slope one side and study the irreducibility of these Hasse polynomials. We will also provide a simple form of all the higher slope Hasse polynomials for $n=3$, answering an open question of Zhang and Feng.
