论文标题
基于强硬木的连续Piatetski-shapiro Primes
Consecutive Piatetski-Shapiro primes based on the Hardy-Littlewood conjecture
论文作者
论文摘要
piatetski-shapiro序列是$ {\ mathcal {n}}}^{（c）}的形式：=（\ lfloor n^c \ rfloor）_ {n = 1}^\ infty $，带有$ c> 1，c> 1，c \ in \ in \ in \ mathbb {在本文中，我们研究了连续的素数的$（p，p，p，p，p，p，p^{\＃}）$，以至于$ p \ in {\ mathcal {n}}}^{（c_1）} $ and $ p^{\ \＃} \ in {对$（p，p，p^{\＃}）$的素数功能的猜想。我们提出了一个启发式论点来支持这一预测，该预测依赖于强烈的耐铁木材猜想的强烈形式。此外，我们证明了与具有复杂指数函数重量的单数序列平均值有关的命题。
The Piatetski-Shapiro sequences are of the form ${\mathcal{N}}^{(c)} := (\lfloor n^c \rfloor)_{n=1}^\infty$ with $c > 1, c \not\in \mathbb{N}$. In this paper, we study the distribution of pairs $(p, p^{\#})$ of consecutive primes such that $p \in {\mathcal{N}}^{(c_1)}$ and $p^{\#} \in {\mathcal{N}}^{(c_2)}$ for $c_1, c_2 > 1$ and give a conjecture with the prime counting functions of the pairs $(p, p^{\#})$. We give a heuristic argument to support this prediction which relies on a strong form of the Hardy-Littlewood conjecture. Moreover, we prove a proposition related to the average of singular series with a weight of a complex exponential function.
