Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions

Details Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions

2005-10-24

arxiv.org/abs/math/0510502v2

Acta Math. 197 (2006), 145-166

Mathematics

Complex Variables

26 pages

Scientific paper

We prove Polya's conjecture of 1943: For a real entire function of order
greater than 2, with finitely many non-real zeros, the number of non-real zeros
of the n-th derivative tends to infinity with n. We use the saddle point method
and potential theory, combined with the theory of analytic functions with
positive imaginary part in the upper half-plane.

Affiliated with

Also associated with

No associations

Rating

Proof of a conjecture of Polya on the zeros of successive derivatives of real 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 Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-523109