Timeline for Arithmetic progressions of gaussian primes
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 23, 2020 at 8:23 | vote | accept | Augusto Santi | ||
| Aug 22, 2020 at 8:40 | comment | added | David Loeffler | You should post that as an answer, it's great | |
| Aug 21, 2020 at 7:28 | comment | added | Christian Elsholtz | A theorem of Tao arxiv.org/abs/math/0501314 says: given any finite sets of points $v_i \in \mathbb{Z}[i]$ there are infinitely many $a \in \mathbb{Z}[i], r \in \mathbb{Z}\setminus \{0\}$ such that all $a+rv_i$ are Gaussian primes. Choosing a shape of two parallel lines, say $v_{1,j}=j, v_{2,j}=i+j, j\in \{1, \ldots , k\}$, shows that there are also long progressions of Gaussian primes not all on the real line, which answers the question left open by David. One could also take lines, say, with 45 degrees angle. | |
| Aug 21, 2020 at 4:59 | vote | accept | Augusto Santi | ||
| Aug 23, 2020 at 8:23 | |||||
| Aug 20, 2020 at 20:03 | history | answered | David Loeffler | CC BY-SA 4.0 |