Timeline for Average value of $\prod_{p|d}{p-1\over p-2}$ for $d=nq$, $n\in{\mathbb N}$, with $p$ odd prime
Current License: CC BY-SA 4.0
9 events
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| Jan 15, 2020 at 4:40 | history | edited | Alex |
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| Jan 10, 2020 at 18:13 | comment | added | Alex | Thanks a lot @reuns for your insight! Could you possibly expand your comment into an answer, especially the $(1)\Rightarrow(2)$ part, so I can upvote... :) It looks less and less likely that someone comes up with a reference for proof of $(2)$... | |
| Jan 9, 2020 at 16:01 | history | edited | Alex | CC BY-SA 4.0 |
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| Jan 8, 2020 at 15:37 | comment | added | Alex | Many thanks! Yes, for odd $q$ the extra factor is $q/\varphi(q)$. For even $q$, it's slightly less pretty. | |
| Jan 8, 2020 at 14:58 | comment | added | reuns | $(1)$ follows from the same Tauberian theorem as in the proof of the PNT. Then for $(2)$ use that $S(nq)= S(q/\gcd(n,q))S(n)$ | |
| Jan 8, 2020 at 14:34 | review | Suggested edits | |||
| Jan 8, 2020 at 15:30 | |||||
| Jan 8, 2020 at 11:58 | comment | added | Sylvain JULIEN | You may also find mathoverflow.net/questions/61842/about-goldbachs-conjecture insightful. | |
| Jan 8, 2020 at 8:21 | comment | added | Sylvain JULIEN | Note that the extra factor equals $q/\varphi(q)$. | |
| Jan 7, 2020 at 23:52 | history | asked | Alex | CC BY-SA 4.0 |