Timeline for Is there always a zero between consecutive local extrema of $\Re \zeta(1/2+it)$ (or $\Im \zeta(1/2+i t)$
Current License: CC BY-SA 3.0
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Jun 24, 2022 at 13:52 | comment | added | Stopple | @sku It sounds like you have questions about the proof in Edwards, possibly for use in your own work. This would make a good MO question, but I can't resolve your questions here in the comments. | |
Jun 24, 2022 at 3:16 | comment | added | sku | @Stopple The proof in Edwards 'Riemann Zeta Function' on page 176, says "if the Riemann hypothesis is true, this derivative is not only positive (because all terms are positive) but also very large [because by von Mangoldt's estimate of N(t) the 𝛼's must be quite dense] between successive zeros of Z". For having the derivative positive all we need are 𝛼−𝑡 being real. I don't think "also very large" part is necessary for the proof. It would be good to get clarity. I am only interested in $t$ real. Edwards needed RH to be true to make $\alpha - t$ terms positive (he needed $t$ real). | |
Jun 23, 2022 at 17:29 | comment | added | Stopple | @sku We have to assume RH to get that $Z^\prime(t)/Z(t)$ is monotone between consecutive zeros. See Edwards book 'Riemann's Zeta Function'. | |
Jun 23, 2022 at 1:59 | comment | added | sku | @Stopple Naive question. Why do we have to assume RH to be true? Aren't all the zeros of $\zeta(0.5 + it)$ on the critical line? | |
S Nov 2, 2017 at 23:18 | history | suggested | jeq | CC BY-SA 3.0 |
Copied images to imgur.com, as they were not being displayed because of new https rule. Added links to original image sources.
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Nov 2, 2017 at 23:05 | review | Suggested edits | |||
S Nov 2, 2017 at 23:18 | |||||
Dec 7, 2013 at 15:23 | comment | added | joro | Does RH imply a Gram point can't be a zeta zero? (about your remark for the simplicity) | |
Aug 17, 2013 at 14:09 | vote | accept | joro | ||
Aug 8, 2013 at 15:05 | history | edited | Stopple | CC BY-SA 3.0 |
Fixed small error re Gram points.
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Aug 5, 2013 at 22:05 | comment | added | Stopple | @joro: I'm working on that now... | |
Aug 5, 2013 at 4:52 | comment | added | joro | Thank you Stopple. There is generalization of this for 0 <= Re(s) <= 1/2 here: mathoverflow.net/questions/138069/… | |
Aug 4, 2013 at 21:07 | history | answered | Stopple | CC BY-SA 3.0 |