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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회지 대한수학회지 제59권 제2호
- 발행연도
- 2022.3
- 수록면
- 299 - 309 (11page)
- DOI
- 10.4134/JKMS.j210123
이용수
초록· 키워드
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Let $k\geqslant 2$ be an integer, $S^k=\{1^k,2^k,3^k,\ldots\}$ and $B=\{b_1,b_2,b_3,\ldots\}$ be an additive complement of $S^k$, which means all sufficiently large integers can be written as the sum of an element of $S^k$ and an element of $B$. In this paper we prove that $$\limsup_{n\rightarrow \infty}\frac{\Gamma\left(2-\frac{1}{k}\right)^{\frac{k}{k-1}}\Gamma\left(1+\frac{1}{k}\right) ^{\frac{k}{k-1}}n^{\frac{k}{k-1}}-b_n}{n} \geqslant \frac{k}{2(k-1)}\frac{\Gamma\left(2-\frac{1}{k}\right)^2}{\Gamma\left(2-\frac{2}{k}\right)},$$ where $\Gamma(\cdot)$ is Euler's Gamma function.
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