Document Type
Article
Date
3-24-2004
Disciplines
Mathematics
Description/Abstract
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 C2 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 {nj} of degrees of polynomials. But for special classes of functions, including the Riemann zeta-function, they hold for all degrees and are asymptotically best possible. From this theory we derive lower estimates for a certain algebraic measure ofa set of values f(E), in terms of the size of the set E.
Recommended Citation
Coman, Dan and Poletsky, Evgeny A., "Transcendence Measures and Algebraic Growth of Entire Functions" (2004). Mathematics - All Scholarship. 16.
https://surface.syr.edu/mat/16
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This manuscript was harvested from arXiv.org, for further information refur to http://arxiv.org/abs/math/0403420