数学
乘法数论
遍历理论
乘法函数
猜想
半群
素数(序理论)
数学证明
离散数学
质数
纯数学
扩展(谓词逻辑)
主要因素
组合数学
数学分析
计算机科学
程序设计语言
几何学
作者
Vitaly Bergelson,Florian Richter
标识
DOI:10.1215/00127094-2022-0055
摘要
We begin by establishing two ergodic theorems which have among their corollaries numerous classical results from multiplicative number theory, including the prime number theorem, a theorem of Pillai and Selberg, a theorem of Erdős and Delange, the mean value theorem of Wirsing, and special cases of the mean value theorem of Halász. Then, 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 that focuses on the disjointness of actions of (N,+) and (N,⋅). We substantiate this extension by providing proofs of several special cases.
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