论文标题
质数定理的动态概括以及添加和乘法半群的脱节性
Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative semigroup actions
论文作者
论文摘要
我们建立了两个千古定理，它们具有乘法数理论的许多经典结果，包括质数定理，Pillai-Selberg定理，Erdős-delange定理，Wirs的平均值定理，以及Halász的平均值定理的特殊情况。通过基于我们的崇高结果背后的想法，我们在一个新的动态框架中重塑了Sarnak的Möbius脱节。这自然会导致萨尔纳克猜想的扩展，该猜想的重点是添加和乘法半群动作的脱节。我们通过提供几种特殊情况的证据来证实这一扩展。
We establish two ergodic theorems which have among their corollaries numerous classical results from multiplicative number theory, including the Prime Number Theorem, a theorem of Pillai-Selberg, a theorem of Erdős-Delange, the mean value theorem of Wirsing, and special cases of the mean value theorem of Halász. By building on the ideas behind our ergodic results, we recast Sarnak's Möbius disjointness conjecture in a new dynamical framework. This naturally leads to an extension of Sarnak's conjecture which focuses on the disjointness of additive and multiplicative semigroup actions. We substantiate this extension by providing proofs of several special cases.
