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Abstract We provide necessary and sufficient conditions for joint ergodicity results for systems of commuting measure preserving transformations for an iterated Hardy field function of polynomial growth. Our method builds on and improves recent techniques due to Frantzikinakis and Tsinas, who dealt with multiple ergodic averages along Hardy field functions; it also enhances an approach introduced by the authors and Ferré Moragues to study polynomial iterates. The more general expression, in which the iterate is a linear combination of a Hardy field function of polynomial growth and a tempered function, is studied as well.
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This content will become publicly available on July 9, 2026
Equidistribution of polynomial sequences in function fields, with applications
We prove a function field analog of Weyl's classical theorem on equidistribution of polynomial sequences. Our result covers the case in which the degree of the polynomial is greater than or equal to the characteristic of the field, which is a natural barrier when applying the Weyl differencing process to function fields. We also discuss applications to van der Corput, intersective and Glasner sets in function fields.
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- PAR ID:
- 10638870
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Advances in mathematics
- Volume:
- 479
- Issue:
- article no. 110424
- ISSN:
- 1090-2082
- Page Range / eLocation ID:
- 44pp
- Subject(s) / Keyword(s):
- Equidistribution function fields intersective sets van der Corput sets Glasner sets
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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