论文标题
Piatetski-Shapiro Prime和几乎是Primes的加性问题
An Additive Problem over Piatetski-Shapiro Primes and Almost-primes
论文作者
论文摘要
令$ \ Mathcal {p} _r $表示几乎可以用$ r $ prime因子，根据多重性计算。在本文中，我们为Piatetski-shapiro Primes $ p = [n^{1/γ}] $建立了Bombieri-Vinogradov类型的定理，并使用$ \ frac {85} {86} {86}<γ<1 $。此外，我们使用此结果来证明，对于$ 0.9989445 <γ<1 $，存在无限的许多piatetski-shapiro Primes，因此$ P+2 = \ Mathcal {p} _3 $，这改善了Lu，Wang和Cai和Peneva的先前结果。
Let $\mathcal{P}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, we establish a theorem of Bombieri-Vinogradov type for the Piatetski-Shapiro primes $p=[n^{1/γ}]$ with $\frac{85}{86}<γ<1$. Moreover, we use this result to prove that, for $0.9989445<γ<1$, there exist infinitely many Piatetski-Shapiro primes such that $p+2=\mathcal{P}_3$, which improves the previous results of Lu, Wang and Cai, and Peneva.
