Digital functions along Squares of Prime Numbers
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908552126267392 |
|---|---|
| author | Drmota, Michael Rivat, Joël |
| author_facet | Drmota, Michael Rivat, Joël |
| contents | In the last 20 years the Gelfond conjectures concerning the well distribution of the sum-of-digits function along prime numbers and along squares have been solved and these results, which are strongly connected with the Sarnak conjecture, were generalized to $q$-multiplicative functions and automatic sequences. In this paper we study a combination of both challenges and prove a Prime Number Theorem for $q$-multiplicative functions along squares which can be rewritten into a well distribution result along squares of primes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Digital functions along Squares of Prime Numbers Drmota, Michael Rivat, Joël Number Theory 11A63, 11L20, 11N05, 11N60, 11L03 In the last 20 years the Gelfond conjectures concerning the well distribution of the sum-of-digits function along prime numbers and along squares have been solved and these results, which are strongly connected with the Sarnak conjecture, were generalized to $q$-multiplicative functions and automatic sequences. In this paper we study a combination of both challenges and prove a Prime Number Theorem for $q$-multiplicative functions along squares which can be rewritten into a well distribution result along squares of primes. |
| title | Digital functions along Squares of Prime Numbers |
| topic | Number Theory 11A63, 11L20, 11N05, 11N60, 11L03 |
| url | https://arxiv.org/abs/2509.17474 |