论文标题
Kloosterman在特征2和3中的Hecke多项式总和
Kloosterman sums and Hecke polynomials in characteristics 2 and 3
论文作者
论文摘要
在本文中，我们对特征2和3的Kloosterman家族的$ K $ TH对称功率$ L $ $ l $ - 功能进行模块化解释，在$ p = 2 $和$ k $的情况下，给出了精确的2-纽顿多边形。我们还对Kloosterman家族的Dwork单位root $ l $ unction进行了$ p $ - ad的模块化解释，并在$ k $奇怪时给出精确的2-纽顿多边形。 在上一篇论文中，我们对Kloosterman家族的对称功率$ l $ lunction的$ Q $ - 亚事牛顿多边形进行了估计，当时$ p \ geq 5 $。我们讨论了不需要对Primes的限制，因此该论文的结果对所有$ p \ geq 2 $。
In this paper we give a modular interpretation of the $k$-th symmetric power $L$-function of the Kloosterman family of exponential sums in characteristics 2 and 3, and in the case of $p=2$ and $k$ odd give the precise 2-adic Newton polygon. We also give a $p$-adic modular interpretation of Dwork's unit root $L$-function of the Kloosterman family, and give the precise 2-adic Newton polygon when $k$ is odd. In a previous paper, we gave an estimate for the $q$-adic Newton polygon of the symmetric power $L$-function of the Kloosterman family when $p \geq 5$. We discuss how this restriction on primes was not needed, and so the results of that paper hold for all $p \geq 2$.
