Document Type

Article

Date

3-24-2004

Embargo Period

11-11-2011

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.

Additional Information

This manuscript was harvested from arXiv.org, for further information refur to http://arxiv.org/abs/math/0403420

Source

Harvested from arXiv.org

Creative Commons License

Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

Included in

Mathematics Commons

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