Transcendence measures and algebraic growth of entire functions

Details Transcendence measures and algebraic growth of entire functions Transcendence measures and algebraic growth of entire functions

2004-03-24

arxiv.org/abs/math/0403420v1

Mathematics

Complex Variables

40 pages

Scientific paper

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 $\zeta$-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 $E$.

Affiliated with

Also associated with

No associations

Rating

Transcendence measures and algebraic growth of entire functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Transcendence measures and algebraic growth of entire functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Transcendence measures and algebraic growth of entire functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-539863