Timeline for Zeroes of a not quite holomorphic (but random if helpful) function
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 30, 2016 at 13:42 | vote | accept | user41147 | ||
| Nov 20, 2016 at 20:52 | comment | added | user41147 | @AlexandreEremenko, thank you so much for your response. You have been enormously helpful. I have been out of action for the last few days so I have not been able to study your answer in any detail yet. However, I can at least quickly answer your question about Kac-polynomials. Terry Tao has a nice discussion on his blog. I also recently came across a question about them here on mathoverflow. | |
| Nov 19, 2016 at 15:43 | comment | added | Alexandre Eremenko | What are "Kac-polynbomials"? | |
| Nov 18, 2016 at 17:41 | comment | added | Alexandre Eremenko | I added a lower estimate. | |
| Nov 17, 2016 at 15:43 | comment | added | user41147 | Yes, sorry, I am being rather vague because I would be happy with various statements. In the case where $p$ and $q$ are assumed to be random polynomials with iid coefficients, then I am interested in the distribution of zeroes in the complex plane. Presumably in this case one would need to assume that the degree $n$ of $p$ and $q$ is large and then take the large $n$ limit in order to make any kind of sharp statement. For low degree polynomials, I would be happy even with a simple condition for the existence of zeroes. | |
| Nov 17, 2016 at 14:37 | comment | added | Alexandre Eremenko | What exactly do you mean by "count"? Estimate their number in terms of degrees of p, q? | |
| Nov 17, 2016 at 14:30 | answer | added | Alexandre Eremenko | timeline score: 14 | |
| Nov 17, 2016 at 14:03 | review | First posts | |||
| Nov 17, 2016 at 14:20 | |||||
| Nov 17, 2016 at 14:02 | history | asked | user41147 | CC BY-SA 3.0 |