Timeline for Positivity of sequences via generating series
Current License: CC BY-SA 2.5
3 events
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| Jul 18, 2010 at 2:55 | comment | added | Qiaochu Yuan | If r is not a polynomial, the coefficients of p(x) r(x)^j will be nonzero infinitely often for sufficiently large j. Unfortunately, they can also be zero infinitely often, so changing the coefficients of A isn't necessarily enough to give you control over the coefficients of p(x) A(r(x)). The SML theorem tells you what kind of control you have and I think one could argue as above, but more carefully. | |
| Jul 18, 2010 at 2:44 | comment | added | Wadim Zudilin | Thanks a lot, Qiaochu! I didn't have your argument to exclude the "eventually" positive ($j\ge i$) case of $p(x)r(x)^j$, but of course I suspect that only "trivial" pairs $p(x),r(x)$ do the job. I am just wondering whether the problem was studied... Can you provide some details on what do you mean by the SML theorem? | |
| Jul 17, 2010 at 22:06 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |