论文标题
Piatetski-shapiro序列的概括（II）
A generalization of Piatetski-Shapiro sequences (II)
论文作者
论文摘要
假设$α，β\ in \ mathbb {r} $。令$α\ geqslant1 $和$ c $为$ 1 <c <12/11 $的真实数字。在本文中，证明在广义的piatetski-shapiro序列中存在无限的数量，该序列由$（\lfloorαn^c+β\ rfloor）_ {n = 1}^\ infty $定义。此外，我们还证明，存在完全由$ c \ in（1，\ frac {19137} {18746}）$的广义piatetski-shapiro序列组成的数量无限的Carmichael编号。这两个定理构成了Guo和Qi先前结果的改进。
Suppose that $α,β\in\mathbb{R}$. Let $α\geqslant1$ and $c$ be a real number in the range $1<c< 12/11$. In this paper, it is proved that there exist infinitely many primes in the generalized Piatetski--Shapiro sequence, which is defined by $(\lfloorαn^c+β\rfloor)_{n=1}^\infty$. Moreover, we also prove that there exist infinitely many Carmichael numbers composed entirely of primes from the generalized Piatetski--Shapiro sequences with $c\in(1,\frac{19137}{18746})$. The two theorems constitute improvements upon previous results by Guo and Qi.
