Synchronizing automatic sequences along Piatetski-Shapiro sequences
Abstract The purpose of this paper is to study subsequences of synchronizing k -automatic sequences ( a ( n )) n ≥0 along Piatetski-Shapiro Sequences ⌊ n c ⌋ with c > 1. In particular we show that ( a (⌊ n c ⌋)) n ≥0 satisfies a prime number theorem of the form ∑ n ≤ x Λ( n ) a (⌊ n c ⌋) ∼ Cx , and, furthermore, that it is deterministic. As an interesting additional result we show that the sequence (⌊ n c ⌋ mod m ) n ≥0 has polynomial subword complexity.
Authors
- Jean‐Marc Deshouillers (ORCID: https://orcid.org/0000-0002-1826-689X)
- Clemens Müllner (ORCID: https://orcid.org/0000-0002-2984-6005)
- Lukas Spiegelhofer (ORCID: https://orcid.org/0000-0003-3552-603X)
- Andrei Shubin (ORCID: https://orcid.org/0000-0002-8702-3218)
- Michael Drmota
Institutions
- Centre National de la Recherche Scientifique (FR)
- TU Wien (AT)
- Université de Bordeaux (FR)
- Montanuniversität Leoben (AT)
- Institut Polytechnique de Bordeaux (FR)
- Institut de Mathématiques de Bordeaux (FR)
Publication Details
- Journal
- Israel Journal of Mathematics
- Published
- 2025-06-29
- DOI
- https://doi.org/10.1007/s11856-025-2755-9
- Primary Topic
- semigroups and automata theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Agence Nationale de la Recherche
- Austrian Science Fund
- Technische Universität Wien