The growth of entire functions of genus zero
| dc.creator | Trong, Dang Duc | |
| dc.creator | Tuyen, Truong Trung | |
| dc.date | 2006-10-01 | |
| dc.date.accessioned | 2026-07-07T07:28:34Z | |
| dc.date.available | 2026-07-07T07:28:34Z | |
| dc.description | In this paper we shall consider the assymptotic growth of $|P_n(z)|^{1/k_n}$ where $P_n(z)$ is a sequence of entire functions of genus zero. Our results extend a result of J. Muller and A. Yavrian. We shall prove that if the sequence of entire functions has a geometric growth at each point in a set $E$ being non-thin at $\infty$ then it has a geometric growth in $\CC$ also. Moreover, if $E$ has some more properties, a similar result also holds for a more general kind of growth. Even in the case where $P_n$ are polynomials, our results are new in the sense that it does not require $k_n\succeq deg(P_n)$ as usually required. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610045 | |
| dc.identifier | http://arxiv.org/abs/math/0610045 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117780 | |
| dc.subject | Complex Variables | |
| dc.subject | 30C85; 30D15; 31A15 | |
| dc.title | The growth of entire functions of genus zero | |
| dc.type | text |