Newton polygons of L-functions of polynomials xᵈ+axᵈ⁻¹ with p≡-1 d

الأصل · EN

For prime p≡-1 d and q a power of p, we obtain the slopes of the q-adic Newton polygons of L-functions of xᵈ+axᵈ⁻¹∈ Fq[x] with respect to finite characters χ when p is larger than an explicit bound depending only on d and ₚ q. The main tools are Dwork's trace formula and Zhu's rigid transform theorem.