Proof of a conjecture of Pólya on the zeros of successive derivatives of real entire functions
نویسندگان
چکیده
We prove Pólya’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 as 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.
منابع مشابه
On the number of real critical points of logarithmic derivatives and the Hawaii conjecture
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