Newton slopes for twisted Artin--Schreier--Witt Towers

Abstract

We fix a monic polynomial $f(x)\in {\mathbb{F}}_q[x]$ over a finite field of characteristic $p$ of degree relatively prime to $p$. Let $a\mapsto \omega (a)$ be the Teichmüller lift of ${\mathbb{F}}_q$, and let $\chi :\mathbb{Z}\to {\mathbb{C}}_p^{\times }$ be a finite character of ${\mathbb{Z}}_p$. The $L$-function associated to the polynomial $f$ and the so-called twisted character ${\omega }^u\times \chi$ is denoted by $L_f({\omega }^u,\chi ,s)$. We prove that, when the conductor of the character is large enough, the $p$-adic Newton slopes of this $L$-function form arithmetic progressions.

References in corpus (2)

• Slopes for higher rank Artin-Schreier-Witt Towers
• The stable property of Newton slopes for general Witt towers