Timeline for Limiting behavior of a sequence of polynomials
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| May 17, 2021 at 19:48 | comment | added | Tom Copeland | As to your question, perhaps something can be gleaned from "On Riemann's zeta function" by Bump and Ng (eudml.org/doc/173728) and "Binomial Polynomials Mimicking Riemann’s Zeta Function" by Coffey and Lettington (arxiv.org/pdf/1703.09251.pdf). | |
| Apr 6, 2021 at 2:06 | comment | added | Richard Stanley | @TomCopeland, of course I was familiar with Rota's statement, but I never understood, nor did I ask him, what it meant. | |
| Apr 6, 2021 at 2:02 | comment | added | Richard Stanley | @AlexandreEremenko, I looked at the uniform distribution on $|z|=1$ and also the eigenvalues of a random $n\times n$ unitary matrix (Haar measure), always with $m=n$, and seemed in both cases to be getting $\cosh(z)$. Admittedly pretty flimsy evidence. I was hoping that for some distribution on $|z|=1$ I would get the same statistical behavior as for the conjectured behavior of the zeros of the Riemann zeta function in the critical strip, or even (really wishful thinking) a simple modification of $\zeta(z)$ itself. | |
| Apr 5, 2021 at 0:18 | comment | added | Tom Copeland | I assume somehow you can relate this to the Appell Hermite polynomials, and that you've explored that already. // Btw, thanks for the answers to some of my questions you've provided and the many resources on the Net. Having been in the thick of it, would you have any more to add to (or subtract from) the discussions in the MO-Q mathoverflow.net/questions/111970/…? | |
| Apr 3, 2021 at 23:15 | comment | added | Alexandre Eremenko | The answer seems to depend strongly on the choice of the sequence $u_j$ and on the relation between $m$ and $n$ as they tend to $\infty$. You should add some assumptions on these for existence of a limit after scaling. | |
| Mar 29, 2021 at 1:42 | history | asked | Richard Stanley | CC BY-SA 4.0 |