On sumsets involving $k$th powers of finite fields
| Autor: | Wu, Hai-Liang, Wei, Ning-Liu, Li, Yu-Bo |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $$\{p\le x: p\equiv1\pmod k; D_k\ \text{has a non-trivial 2-additive decomposition}\}.$$ |
| Databáze: | arXiv |
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