Weighted uniform distribution of subpolynomial functions along primes and applications
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909803942510592 |
|---|---|
| author | Bergelson, Vitaly Kolesnik, Grigori Son, Younghwan |
| author_facet | Bergelson, Vitaly Kolesnik, Grigori Son, Younghwan |
| contents | Let $u(x)$ be a subpolynomial function in a Hardy field. We establish necessary and sufficient conditions for the weighted uniform distribution of the sequences $(u(n))_{n\in\mathbb{N}}$ and $(u(p_n))_{n\in\mathbb{N}}$, where $p_n$ denotes the $n$-th prime. This extends the main result of [4] to the weighted setting and leads to new applications in uniform distribution theory, ergodic theory, and additive combinatorics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19722 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted uniform distribution of subpolynomial functions along primes and applications Bergelson, Vitaly Kolesnik, Grigori Son, Younghwan Number Theory Dynamical Systems Let $u(x)$ be a subpolynomial function in a Hardy field. We establish necessary and sufficient conditions for the weighted uniform distribution of the sequences $(u(n))_{n\in\mathbb{N}}$ and $(u(p_n))_{n\in\mathbb{N}}$, where $p_n$ denotes the $n$-th prime. This extends the main result of [4] to the weighted setting and leads to new applications in uniform distribution theory, ergodic theory, and additive combinatorics. |
| title | Weighted uniform distribution of subpolynomial functions along primes and applications |
| topic | Number Theory Dynamical Systems |
| url | https://arxiv.org/abs/2509.19722 |