On the k-resultant modulus set problem on varieties over finite fields

2021/09/28 by Minh Quy Pham, Pham, Minh Quy
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.2109.13506

11 pages

arxiv created 2021/09/28 · openalex publication_date 2021/09/28 · arxiv updated 2021/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let V⊂ \mathbbF_q^d be a regular variety, k≥ 3 is an integer and A⊆ V. Covert, Koh, and Pi (2017) proved the following generalization of the Erdős-Falconer distance problem: If |A|≫ q^{(d-1)/(2)+(1)/(k-1)}, then we have Δ_k(A)=\|x₁+⋯+x_k|\colon x_i∈ A\⊇ \mathbbF_q^*. In this paper, we provide improvements and extensions of their result.

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