论文标题
Möbius函数的平均值在变化的素数上
Averages of the Möbius function on shifted primes
论文作者
论文摘要
民间传说的猜想是，莫比乌斯的功能在变化的素数上取消了。也就是说，$ \ sum_ {p \ le x}μ（p+h）\ = \ o（π（x））$ as $ x \ to \ to \ infty $对于任何固定的换档$ h> 0 $。这至少是自1989年希尔德布兰德（Hildebrand）以来的印刷。我们证明了Shifts $ h \ le H $的猜想，提供了$ \ log H/\ log \ log \ log x \ to \ infty $。我们还获得了Prime $ K $ TUPLASS的偏移结果，以及Möbius与Von Mangoldt和Divisor功能的更高相关性。我们的论点将筛子方法与Matomäki，Radziwiłł和Tao的作品相结合，以平均的Chowla猜想形式。
It is a folklore conjecture that the Möbius function exhibits cancellation on shifted primes; that is, $\sum_{p\le X}μ(p+h) \ = \ o(π(X))$ as $X\to\infty$ for any fixed shift $h>0$. This appears in print at least since Hildebrand in 1989. We prove the conjecture on average for shifts $h\le H$, provided $\log H/\log\log X\to\infty$. We also obtain results for shifts of prime $k$-tuples, and for higher correlations of Möbius with von Mangoldt and divisor functions. Our argument combines sieve methods with a refinement of Matomäki, Radziwiłł, and Tao's work on an averaged form of Chowla's conjecture.
