Newton polygons of $L$-functions of polynomials $x^d+ax^{d-1}$ with $p\equiv-1\bmod d$

Abstract

For prime p ≡ −1 mod d and q a power of p, we obtain the slopes of the q-adic Newton polygons of L-functions of x d +ax d−1 ∈ Fq[x] with respect to finite characters χ 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.