Newton polygons of $L$-functions of polynomials $x^d+a{x}^{d-1}$ with $p\equiv -1\mathrm{mod}d$

Abstract

For prime $p\equiv -1\mathrm{mod}d$ and $q$ a power of $p$, we obtain the slopes of the $q$-adic Newton polygons of $L$-functions of $x^d+a{x}^{d-1}\in {\mathbb{F}}_q[x]$ with respect to finite characters $\chi$ when $p$ is larger than an explicit bound depending only on $d$ and ${\log }_{p}q$. The main tools are Dwork's trace formula and Zhu's rigid transform theorem.

arXiv comment8 pages

References in corpus (1)

• Asymptotic variation of L-functions of exponential sums