On the Newton polygons of twisted L-functions of binomials

2021/09/30 by Shenxing Zhang, Zhang, Shenxing
Computer Science · Mathematics · #11L07 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2109.14852

openalex publication_date 2021/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let χ be an order c multiplicative character of a finite field and f(x)=x^d+λx^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\bmod 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.

Citations

• T-adic exponential sums under diagonal base change

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