Work

Ergodic averages along sequences of slow growth

Year: 2025

Type: article

Abstract: We consider pointwise almost everywhere convergence of weighted ergodic averages along the sequence , where denotes the number of prime factors of counted with multiplicities. It was previously shown that a pointwise ergodic theorem for functions does not hold along . We classify the strength of this divergence by proving a double‐logarithmic pointwise ergodic theorem for functions along . This contrasts the behavior of Khintchine‐type averages, for which, under any weaker form of averaging, there exists a bounded measurable function for which almost everywhere convergence fails. Moreover, we show that certain perturbations of increasing subpolynomial sequences fail to satisfy a pointwise ergodic theorem, yielding natural new examples of such sequences.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70124

Authors: Kaitlyn Loyd, Sovanlal Mondal

Institutions: University of Maryland, College Park, The Ohio State University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: National Science Foundation