Timeline for Fully explicit Linnik's Theorem
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 31 at 23:25 | comment | added | GH from MO | Please use a high-level tag like "nt.number-theory". I added this tag now. Regarding high-level tags, see meta.mathoverflow.net/q/1075 | |
| Mar 31 at 23:25 | history | edited | GH from MO |
edited tags
|
|
| Mar 31 at 23:02 | comment | added | Zach Hunter | have you seen the recent paper: arxiv.org/pdf/2401.17570.pdf ? | |
| Mar 31 at 22:39 | answer | added | Mehdi Hassani | timeline score: 4 | |
| Jul 22, 2022 at 3:08 | comment | added | efs | @2734364041 I explicitely meant IN the wikipedia article, as the op claimed. | |
| Jul 21, 2022 at 20:14 | comment | added | 2734364041 | @efs Writing Linnik's bound as $cm^L$, it is clear from a careful read of the introduction to Heath-Brown's paper that he only computes $L$ for all $m\geq 2$. On the other hand, it follows from Heath-Brown's paper (dig into the details) that there exists an absolute and effectively computable constant $m_0\geq 2$ such that if $m\geq m_0$, then one can take $c=1$. That being said, in order to use Heath-Brown's value (or Xylouris's improved value) of $L$, one must take $m_0$ to be epically gigantic. | |
| Jul 11, 2021 at 21:23 | comment | added | Woett | I really don't see how it does. Those 3 theorems don't mention Linnik's Theorem and specifically talk about 'sufficiently large' moduli. | |
| Jul 11, 2021 at 19:17 | comment | added | efs | If I'm not wrong, Heath-Brown's article gives numerical values for the $c$'s involved. See Theorems 1, 2 and 3. | |
| Jul 11, 2021 at 19:02 | comment | added | Woett | The Wikipedia article says 'Linnik's proof showed c and L to be effectively computable' and 'in Heath-Brown's result the constant c is effectively computable.' And, for example, the most recent paper by Matti Jutila that is mentioned and referenced on the Wikipedia page also states 'everything can be made explicit. In fact it would not be too difficult to calculate'. But I have not been able to actually find such a calculation yet. | |
| Jul 11, 2021 at 18:35 | comment | added | efs | Where does the wikipedia article claim that "in certain cases both these constants c and L can be made explicit" without a reference? | |
| Jul 11, 2021 at 17:37 | history | asked | Woett | CC BY-SA 4.0 |