On the Newton polygons of twisted L-functions of binomials

摘要

Let chi be an order c multiplicative character of a finite field and f(x) = x(d) + lambda x(e) 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 p mod cd.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.

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