Timeline for what is the solutions of function equation
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 17, 2019 at 1:11 | history | edited | zhizhi Liu | CC BY-SA 4.0 |
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| Mar 21, 2017 at 21:06 | history | edited | zhizhi Liu | CC BY-SA 3.0 |
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| Mar 21, 2017 at 20:51 | comment | added | T. Amdeberhan | For the critical line, you solve $\sqrt2\sin(y\log2)+\sqrt3\sin(y\log3)=0$; equivalently, one checks whether $f_1:=\sqrt2\sin(y\log2)$ and $f_2=\sqrt3\sin(y(-\log3))$ meet. But, that is true: any two $\sin$ waves (in this case of different frequencies) meet (and infinitely often). So, there are infinitely many solutions on the critical line. | |
| Mar 21, 2017 at 20:27 | comment | added | Qfwfq | "Functional equations"?? | |
| Mar 21, 2017 at 20:20 | answer | added | paul garrett | timeline score: 4 | |
| Mar 21, 2017 at 17:35 | comment | added | juan | Yes. You have reason. | |
| Mar 21, 2017 at 17:21 | comment | added | Igor Rivin | @juan Ah, I see. Anyway, it sounds like looking for a zero off the line might be futile :) | |
| Mar 21, 2017 at 17:04 | comment | added | juan | I was trying to find the first zero off the line. This needs no explanation. I have only to show it. But it is not so easy. Perhaps the question is more interesting that I thought. | |
| Mar 21, 2017 at 17:02 | comment | added | juan | They are the zeros of $\sqrt{2}\sin(t\log2)-\sqrt{3}\sin(t\log3)$. I make some plots. A complex zero of this function will be "visible" in the real plot. Again this have a long justification. Each time the function decreases it cuts the real axis. each time the function increases cuts the real axis. (I have no time for English grammar). | |
| Mar 21, 2017 at 16:55 | comment | added | Igor Rivin | @juan How do you know? | |
| Mar 21, 2017 at 16:55 | comment | added | juan | All solutions with $ |\Im(z)|\le 7000$ are on the critical line. | |
| Mar 21, 2017 at 16:03 | history | edited | zhizhi Liu | CC BY-SA 3.0 |
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| Mar 21, 2017 at 15:56 | history | asked | zhizhi Liu | CC BY-SA 3.0 |