Timeline for On the prime number theorem in arithmetic progression
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 24, 2013 at 20:03 | vote | accept | Marco Cantarini | ||
| Oct 24, 2013 at 16:44 | comment | added | Marco Cantarini | @GregMartin and thank you for your clarifications! | |
| Oct 24, 2013 at 16:43 | comment | added | Marco Cantarini | @GHfromMO Thank you for your answers! | |
| Oct 22, 2013 at 17:04 | comment | added | GH from MO | @The_Cam: Greg Martin is right. If we knew the bound $\pi(x;q,a) \gg \frac1{\phi(q)}\frac x{\log x}$, then for any $\epsilon>0$ we would know that $\pi(x;q,a)>0$ for some $x\ll_\epsilon q^{1+\epsilon}$. However, this consequence is only known for $x\ll q^{5.2}$ at the moment, see en.wikipedia.org/wiki/Linnik%27s_theorem | |
| Oct 22, 2013 at 9:58 | comment | added | Greg Martin | For fixed $q$, yes, this follows from the asymptotic formula. But if $q$ can grow with $x$, then we don't know this lower bound in all ranges. | |
| Oct 21, 2013 at 23:01 | comment | added | Marco Cantarini | @GregMartin see this link academic.csuohio.edu/soprunov_i/pdf/primes.pdf | |
| Oct 21, 2013 at 19:55 | comment | added | Greg Martin | It is not true that we know the lower bound $\pi(x;q,a) \gg \frac1{\phi(q)}\frac x{\log x}$ for all ranges of $q$ and $x$. (By the way, the notation $\pi(x;q,a)$ is more standard than $\pi(x,a,q)$.) | |
| Oct 21, 2013 at 14:39 | answer | added | GH from MO | timeline score: 11 | |
| Oct 21, 2013 at 13:39 | comment | added | Dimitris Koukoulopoulos | Look up "Brun-Tithcmarsch inequality". | |
| Oct 21, 2013 at 12:45 | answer | added | H.Flip | timeline score: 4 | |
| Oct 21, 2013 at 12:23 | comment | added | Alvin | It is a consequence of Dirichlet's theorem on arithmetic progressions. | |
| S Oct 21, 2013 at 11:42 | history | suggested | Konstantinos Gaitanas | CC BY-SA 3.0 |
Some corrections are needed
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| Oct 21, 2013 at 11:26 | review | Suggested edits | |||
| S Oct 21, 2013 at 11:42 | |||||
| Oct 21, 2013 at 11:12 | review | First posts | |||
| Oct 21, 2013 at 11:13 | |||||
| Oct 21, 2013 at 10:55 | history | asked | Marco Cantarini | CC BY-SA 3.0 |