Gaussian almost primes in almost all narrow sectors
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916359222329344 |
|---|---|
| author | Järviniemi, Olli Teräväinen, Joni |
| author_facet | Järviniemi, Olli Teräväinen, Joni |
| contents | We show that almost all sectors of the disc $\{z \in \mathbb{C}: |z|^2\leq X\}$ of area $(\log X)^{15.1}$ contain products of exactly two Gaussian primes, and that almost all sectors of area $(\log X)^{1 + \varepsilon}$ contain products of exactly three Gaussian primes. The argument is based on mean value theorems, large value estimates and pointwise bounds for Hecke character sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_05822 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gaussian almost primes in almost all narrow sectors Järviniemi, Olli Teräväinen, Joni Number Theory We show that almost all sectors of the disc $\{z \in \mathbb{C}: |z|^2\leq X\}$ of area $(\log X)^{15.1}$ contain products of exactly two Gaussian primes, and that almost all sectors of area $(\log X)^{1 + \varepsilon}$ contain products of exactly three Gaussian primes. The argument is based on mean value theorems, large value estimates and pointwise bounds for Hecke character sums. |
| title | Gaussian almost primes in almost all narrow sectors |
| topic | Number Theory |
| url | https://arxiv.org/abs/2303.05822 |