A note on exponential-Möbius sums over \mathbbF_q[t]

2017/11/23 by Sam Porritt, Porritt, Sam
Computer Science · Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1711.08729

openalex publication_date 2017/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1991, Baker and Harman proved, under the assumption of the generalized Riemann hypothesis, that max _{θ∈ [0,1)} |∑ _{n ≤ x} μ(n) e(n θ) | ≪_εx^{3/4 + ε}. The purpose of this note is to deduce an analogous bound in the context of polynomials over a finite field using Weil's Riemann Hypothesis for curves over a finite field. Our approach is based on the work of Hayes who studied exponential sums over irreducible polynomials.

Citations

• Linear and quadratic uniformity of the Möbius function over \mathbbF_q[t]

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