论文标题
导致Mobius功能过时的素数
Result on the Mobius Function over Shifted Primes
论文作者
论文摘要
本文提供了用于示例Mobius函数$ \ sum_ {p \ leq x}μ（p+a）= o \ left的新渐近结果在转移的素数上，$ a \ ne0 $是固定参数，而$ c> 1 $是任意常数。这些结果改善了当前估计值$ \ sum_ {p \ leq x}μ（p+a）=（1-δ）π（x）$，和$ \ sum_ {p \ leq x}λ（p+a）=（p+a）=（1-δ）π（x）π（x）$分别为$δ> 0 $。此外，自相关功能的有条件证明$ \ sum_ {p \ leq x}μ（p+a）μ（p+b）= o \ left（x（x（x \ log x）^{ - c} \ right）$，以及自动化功能的无条件证明$ \ sum sum \ sum p+a} p+b） \ left（x（x（\ log x）^{ - c} \右）$上的$ a \ ne b $，也包括在内。
This article provides new asymptotic results for the summatory Mobius function $\sum_{p \leq x} μ(p+a) =O \left (x(\log x)^{-c} \right )$ and the summatory Liouville function $\sum_{p \leq x} λ(p+a) =O \left (x(\log x)^{-c} \right )$ over the shifted primes, where $a\ne0$ is a fixed parameter, and $c>1$ is an arbitrary constant. These results improve the current estimates $\sum_{p \leq x} μ(p+a)=(1-δ)π(x)$, and $\sum_{p \leq x} λ(p+a)=(1-δ)π(x)$ for $δ>0$, respectively. Furthermore, a conditional proof for the autocorrelation function $\sum_{p \leq x} μ(p+a)μ(p+b) =O \left (x(\log x)^{-c} \right )$, and an unconditional proof for the autocorrelation function $\sum_{p \leq x} λ(p+a)λ(p+b) =O \left (x(\log x)^{-c} \right )$ over the shifted primes, where $a\ne b$, are also included.
