English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We establish two ergodic theorems which have among their corollaries numerousclassical results from multiplicative number theory, including the Prime NumberTheorem, a theorem of Pillai-Selberg, a theorem of Erd\H{o}s-Delange, the meanvalue theorem of Wirsing, and special cases of the mean value theorem ofHal\'asz. By building on the ideas behind our ergodic results, we recastSarnak's M\"obius disjointness conjecture in a new dynamical framework. Thisnaturally leads to an extension of Sarnak's conjecture which focuses on thedisjointness of additive and multiplicative semigroup actions. We substantiatethis extension by providing proofs of several special cases.

Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative semigroup actions