Generic Newton Slopes for Artin-Schreier-Witt Tower in two variables

2016/12/21 by Zhu, Hui June
#11 #14 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1612.07158

Abstract

We prove that for any generic polynomial f in two variables of degree (d₁,d₂) over the rationals, for p large enough the Newton slopes of the character power series C_f^*(χ_m,s) of f at p is independent of the choice of the character χ_m (of conductor p^m); and the Newton slopes of the L-function L_f^*(χ_m,s) of f at p is in weighted arithmetic progression.

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