Local mean value estimates for Weyl sums

2023/03/21 by Julia Brandes, Changhao Chen, Brandes, Julia +3 · 1 citation
Mathematics · #11D45 #Advanced Algebra and Geometry #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Primary: 11L15 #Secondary: 11L07

paper · pdf · doi:10.48550/arxiv.2303.11913

openalex publication_date 2023/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We obtain new estimates - both upper and lower bounds - on the mean values of the Weyl sums over a small box inside of the unit torus. In particular, we refine recent conjectures of C. Demeter and B. Langowski (2022), and improve some of their results.

Cited by

• An extended Vinogradov's mean value theorem

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• Restricted mean value theorems and metric theory of restricted Weyl sums
• Mean value theorems for rational exponential sums
• Optimal mean value estimates for the quadratic Weyl sums in two dimensions
• Estimates for smooth Weyl sums on major arcs
• A remark on the mean value inequalities related to Waring's problem