Transcendence measures and algebraic growth of entire functions
| dc.creator | Coman, Dan | |
| dc.creator | Poletsky, Evgeny A. | |
| dc.date | 2004-03-24 | |
| dc.date.accessioned | 2026-07-07T05:06:43Z | |
| dc.date.available | 2026-07-07T05:06:43Z | |
| dc.description | In this paper we obtain estimates for certain transcendence measures of an entire function $f$. Using these estimates, we prove Bernstein, doubling and Markov inequalities for a polynomial $P(z,w)$ in ${\Bbb C}^2$ along the graph of $f$. These inequalities provide, in turn, estimates for the number of zeros of the function $P(z,f(z))$ in the disk of radius $r$, in terms of the degree of $P$ and of $r$. Our estimates hold for arbitrary entire functions $f$ of finite order, and for a subsequence $\{n_j\}$ of degrees of polynomials. But for special classes of functions, including the Riemann $ζ$-function, they hold for all degrees and are asymptotically best possible. From this theory we derive lower estimates for a certain algebraic measure of a set of values $f(E)$, in terms of the size of the set $E$. | |
| dc.description | 40 pages | |
| dc.identifier | https://arxiv.org/abs/math/0403420 | |
| dc.identifier | http://arxiv.org/abs/math/0403420 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70580 | |
| dc.subject | Complex Variables | |
| dc.subject | Number Theory | |
| dc.subject | Primary: 30D15; Secondary: 11J99, 30D20 | |
| dc.title | Transcendence measures and algebraic growth of entire functions | |
| dc.type | text |