Newton slopes for twisted Artin–Schreier–Witt towers

Abstract

We fix a monic polynomial [Formula: see text] over a finite field of characteristic [Formula: see text] of degree relatively prime to [Formula: see text]. Let [Formula: see text] be the Teichmüller lift of [Formula: see text], and let [Formula: see text] be a finite character of [Formula: see text]. The [Formula: see text]-function associated to the polynomial [Formula: see text] and the so-called twisted character [Formula: see text] is denoted by [Formula: see text] (see Definition 1.2). We prove that, when the conductor of the character is large enough, the [Formula: see text]-adic Newton slopes of this [Formula: see text]-function form arithmetic progressions.