Ultra-short sums of trace functions

2023/02/27 by Emmanuel Kowalski, Kowalski, Emmanuel, Théo Untrau +1 · 1 citation
Mathematics · #11L15 #11T23 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2302.13670

openalex publication_date 2023/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize results of Duke, Garcia, Hyde, Lutz and others on the distribution of sums of roots of unity related to Gaussian periods to obtain equidistribution of similar sums over zeros of arbitrary integral polynomials. We also interpret these results in terms of trace functions, and generalize them to higher rank trace functions.

Cited by

• Wasserstein metrics and quantitative equidistribution of exponential sums over finite fields

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