Pseudorandomness of primes at large scales
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917845644869632 |
|---|---|
| author | Leung, Sun-Kai |
| author_facet | Leung, Sun-Kai |
| contents | Assuming a $q$-variant of the prime $k$-tuple conjecture uniformly, we compute mixed moments of the number of primes in disjoint short intervals and progressions, respectively. This involves estimating the mean of singular series along products of lattices, which is of independent interest. As a consequence, we establish the convergence of both sequences of suitably normalized primes to a standard Poisson point process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05380 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pseudorandomness of primes at large scales Leung, Sun-Kai Number Theory Probability 11N05, 60G55 Assuming a $q$-variant of the prime $k$-tuple conjecture uniformly, we compute mixed moments of the number of primes in disjoint short intervals and progressions, respectively. This involves estimating the mean of singular series along products of lattices, which is of independent interest. As a consequence, we establish the convergence of both sequences of suitably normalized primes to a standard Poisson point process. |
| title | Pseudorandomness of primes at large scales |
| topic | Number Theory Probability 11N05, 60G55 |
| url | https://arxiv.org/abs/2407.05380 |