Averages over the Gaussian Primes: Goldbach's Conjecture and Improving Estimates
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_ | 1866913274117750784 |
|---|---|
| author | Giannitsi, Christina Krause, Ben Lacey, Michael Mousavi, Hamed Rahimi, Yaghoub |
| author_facet | Giannitsi, Christina Krause, Ben Lacey, Michael Mousavi, Hamed Rahimi, Yaghoub |
| contents | We prove versions of Goldbach conjectures for Gaussian primes in arbitrary sectors. Fix an interval $ω\subset \mathbb{T}$. There is an integer $N_ω$, so that every odd integer $n$ with $N(n)>N_ω$ and $\text{dist}( \text{arg}(n) , \mathbb{T}\setminus ω) > (\log N(n)) ^{-B}$, is a sum of three Gaussian primes $n=p_1+p_2+p_3$, with $\text{arg}(p_j) \in ω$, for $j=1,2,3$. A density version of the binary Goldbach conjecture in a sector is also proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14249 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Averages over the Gaussian Primes: Goldbach's Conjecture and Improving Estimates Giannitsi, Christina Krause, Ben Lacey, Michael Mousavi, Hamed Rahimi, Yaghoub Number Theory Classical Analysis and ODEs We prove versions of Goldbach conjectures for Gaussian primes in arbitrary sectors. Fix an interval $ω\subset \mathbb{T}$. There is an integer $N_ω$, so that every odd integer $n$ with $N(n)>N_ω$ and $\text{dist}( \text{arg}(n) , \mathbb{T}\setminus ω) > (\log N(n)) ^{-B}$, is a sum of three Gaussian primes $n=p_1+p_2+p_3$, with $\text{arg}(p_j) \in ω$, for $j=1,2,3$. A density version of the binary Goldbach conjecture in a sector is also proved. |
| title | Averages over the Gaussian Primes: Goldbach's Conjecture and Improving Estimates |
| topic | Number Theory Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2309.14249 |