On the Newton polygons of twisted L-functions of binomials

Abstract

Let χ be an order c multiplicative character of a finite field and f(x)=xd+λxe a binomial with (d,e)=1. We study the twisted classical and T-adic Newton polygons of f. When p>(d−e)(2d−1), we give a lower bound of Newton polygons and show that they coincide if p does not divide a certain integral constant depending on pmodcd. We conjecture that this condition holds if p is large enough with respect to c,d by combining all known results and the conjecture given by Zhang-Niu. As an example, we show that it holds for e=d−1.