Timeline for The prime numbers modulo $k$, are not periodic
Current License: CC BY-SA 3.0
21 events
| when toggle format | what | by | license | comment | |
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| May 28, 2014 at 19:47 | answer | added | Lucia | timeline score: 26 | |
| May 28, 2014 at 18:39 | comment | added | Benjamin Dickman | Although there are already a couple of unconditional proofs, it seems to me that the result follows from a positive answer to this MO question from a few days earlier: mathoverflow.net/q/168109/22971 | |
| May 28, 2014 at 17:12 | comment | added | David E Speyer | In particular, Lucia's answer there looks adaptable: Show that it is impossible for both $\sum_{n \leq N} \chi(n)$ and $\sum_{p \leq N} \chi(p) \log p$ to be $O(N^{1/2-\delta})$, for some Dirichlet character $\chi$. | |
| May 28, 2014 at 15:35 | comment | added | Terry Tao | Related (in view of Lucia's comments): mathoverflow.net/questions/13647/… | |
| S May 28, 2014 at 15:26 | history | suggested | Solaris | CC BY-SA 3.0 |
Modified it slightly
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| May 28, 2014 at 15:20 | review | Suggested edits | |||
| S May 28, 2014 at 15:26 | |||||
| May 28, 2014 at 15:08 | comment | added | Douglas Zare | @Jeff Strom: Preperiodic means there may be some prefix attached to a periodic part. You called this eventually periodic. | |
| May 28, 2014 at 14:50 | comment | added | Jeff Strom | @DouglasZare: what does preperiodic mean? | |
| May 28, 2014 at 3:16 | comment | added | Douglas Zare | The question should ask whether the sequence is preperiodic rather than periodic. | |
| S May 28, 2014 at 2:53 | history | suggested | Solaris | CC BY-SA 3.0 |
Added a question
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| May 28, 2014 at 2:33 | review | Suggested edits | |||
| S May 28, 2014 at 2:53 | |||||
| May 28, 2014 at 2:06 | answer | added | Jeff Strom | timeline score: 4 | |
| May 28, 2014 at 2:02 | comment | added | Noah Schweber | The way the problem is phrased sounds like a homework problem, but I think that's not the case - this looks interesting! | |
| S May 28, 2014 at 1:59 | history | suggested | Puraṭci Vinnani | CC BY-SA 3.0 |
Improved notation.
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| May 28, 2014 at 1:40 | review | Suggested edits | |||
| S May 28, 2014 at 1:59 | |||||
| May 28, 2014 at 0:42 | comment | added | Lucia | Here are two proofs but neither is very elementary. First, Daniel Shiu has shown that there are arbitrarily long strings of consecutive primes congruent to any given $a \pmod q$. Second, if the primes were periodic $\pmod q$, then pick a non-trivial complex character $\pmod q$ and the criterion implies that $\log L(s,\chi)$ is analytic in Re$(s)>1/3$ say, and hence the corresponding $L$-function cannot have any non-trivial zeros. (You can also argue with the quadratic $L$-function, but then the prime squares have to be kept in mind.) Probably I'm missing the obvious elementary proof! | |
| May 28, 2014 at 0:41 | review | Close votes | |||
| May 28, 2014 at 5:04 | |||||
| May 28, 2014 at 0:27 | comment | added | Lucia | This seems like a perfectly fine question to me. Why the down & close vote? | |
| May 28, 2014 at 0:25 | comment | added | Anthony Quas | This is not a research question. You could try math.stackexchange.com | |
| May 28, 2014 at 0:04 | review | First posts | |||
| May 28, 2014 at 0:15 | |||||
| May 27, 2014 at 23:41 | history | asked | solaris | CC BY-SA 3.0 |