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arXiv · 2304.11789

On sumsets involving $k$th powers of finite fields

Hai-Liang Wu·Ning-Liu Wei·Yu-Bo Li
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Abstract

In this paper, we study some topics concerning the additive decompositions of the set $D_k$ of all $k$th power residues modulo a prime $p$. For example, given a positive integer $k\ge2$, we prove that $$\lim_{x\rightarrow+\infty}\frac{B(x)}{\pi(x)}=0,$$ where $\pi(x)$ is the number of primes $p\le x$ and $B(x)$ denotes the cardinality of the set $$\{p\le x: p\equiv1\pmod k; D_k\ \text{has a non-trivial 2-additive decomposition}\}.$$

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Hai-Liang Wu, Ning-Liu Wei, Yu-Bo Li. 2023-04-24. On sumsets involving $k$th powers of finite fields. https://doi.org/10.1016/j.disc.2024.113870

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