On sumsets involving kth powers of finite fields

2023/04/24 by Hai-Liang Wu, Ning-Liu Wei, Yu-Bo Li +1
Computer Science · Mathematics · #Coding theory and cryptography #Limits and Structures in Graph Theory #Analytic Number Theory Research

paper · pdf · doi:10.1016/j.disc.2024.113870

Abstract

In this paper, we study some topics concerning the additive decompositions of the set D_k of all kth power residues modulo a prime p. For example, given a positive integer k≥2, we prove that lim_x→+∞(B(x))/(π(x))=0, where π(x) is the number of primes p≤ x and B(x) denotes the cardinality of the set \p≤ x: p≡1\pmod k; D_k has a non-trivial 2-additive decomposition\.

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