Timeline for Are the zeros of the sum/difference of these integrals all on the critical line?
Current License: CC BY-SA 3.0
22 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Aug 22, 2013 at 10:11 | comment | added | Agno | Joro, I do not have a formally published reference, but I found the formula when I was deriving the "Integer Counting function" (link in the OP) here: mathworld.wolfram.com/SawtoothWave.html. Note that there is another function listed that uses $\tan^{-1}$ and $\cot$. Have not tried that in an integral yet. | |
| Aug 22, 2013 at 9:26 | comment | added | joro | It is partially optimistic that maple correctly computes some {x} integrals correctly, very interesting! Is there a published reference for your {x} ? | |
| Aug 22, 2013 at 8:40 | comment | added | Agno | Thanks Joro. Good idea to take the integral question separately. I am still curious to understand more about this integral and the ambivalence in evaluating it. | |
| Aug 22, 2013 at 8:19 | comment | added | joro | Agno, I asked extended question for your method for the fractional part: mathoverflow.net/questions/140084/… | |
| Aug 22, 2013 at 7:04 | comment | added | joro | Agno you are welcome. Btw, just for a change why don't you try do disprove RH via zeros of some obscure function off the line ;-) | |
| Aug 22, 2013 at 6:50 | history | edited | Agno | CC BY-SA 3.0 |
Added that zeros have been found and conjecture is false.
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| Aug 22, 2013 at 6:46 | vote | accept | Agno | ||
| Aug 22, 2013 at 6:46 | comment | added | Agno | Joro, that clearly proofs the conjecture wrong and new scars have been created... Anyway, your help has been much appreciated! | |
| Aug 22, 2013 at 6:04 | comment | added | joro | Agno sorry, my mistake, didn't notice the critical strip. Edited the answer with zeros in the critical strip. | |
| Aug 21, 2013 at 22:38 | history | edited | Agno | CC BY-SA 3.0 |
Added a comment/warning/question about evaluating the integrals at infinity.
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| Aug 21, 2013 at 21:43 | comment | added | Agno | Many thanks, Joro. Always a pleasure to see the Master of Root finding in action. Looking at some of my scars from earlier discussions with you, I decided this time to explicitly limit my conjecture to the Critical Strip only ;-) Delighted to see that you did not discover (yet) any other zeros in the strip than those lying on the critical line! | |
| Aug 21, 2013 at 12:29 | comment | added | joro | Agno, computing I(s) via zeta got some zeros off the critical line and edited the answer. | |
| Aug 20, 2013 at 7:53 | history | edited | Agno | CC BY-SA 3.0 |
Fixed minus sign in front of e
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| Aug 19, 2013 at 18:49 | history | edited | Agno | CC BY-SA 3.0 |
Removed the $\frac12$ from the term in the integral $(x-1/2)$
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| Aug 19, 2013 at 18:37 | comment | added | Agno | Joro. I found the problem. The $\frac12$ should not be subtracted form the $x$. I tried it in Wolfram Alpha and this works. Here is the code for $\zeta(3)$ till $x=9$ : 3/(3-1)-1/2-(3*i)/(2*π)*(integral from 1..9 of ln(-e^(-2*π*i*(x)))/(x^(3+1))) | |
| Aug 19, 2013 at 14:45 | comment | added | joro | Agno, I can't compute $I(s)$. Would you please give the values of $I(3), I(1/2 + 13.35 i), I(1/2 + 20 i)$, the method to compute them and to what precision they are correct? Thank you. | |
| Aug 19, 2013 at 12:36 | history | edited | Agno | CC BY-SA 3.0 |
Fixed the error that integrals were starting at 0 instead of 1 + added range of validity (Re(s) .>= 0)
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| Aug 19, 2013 at 12:30 | history | edited | Agno | CC BY-SA 3.0 |
Fixed the error that integrals were starting at 0 instead of 1
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| Aug 19, 2013 at 7:58 | answer | added | joro | timeline score: 3 | |
| Aug 18, 2013 at 14:39 | history | asked | Agno | CC BY-SA 3.0 |