An Extremal Property of Entire Functions with Positive Zeros

Asymptotics of Zeros for Some Entire Functions

We study the asymptotics of zeros for entire functions of the form sin z+ ∫ 1 −1 f(t)e dt with f belonging to a space X →֒ L1(−1, 1) possessing some minimal regularity properties.

Convolution Operators and Zeros of Entire Functions

Let G(z) be a real entire function of order less than 2 with only real zeros. Then we classify certain distributions functions F such that the convolution (G ∗ dF )(z) = ∫∞ −∞G(z − is) dF (s) has only real zeros.

An extremal problem for a class of entire functions

Let f be an entire function of the exponential type, such that the indicator diagram is in [−iσ, iσ ], σ > 0. Then the upper density of f is bounded by cσ , where c≈ 1.508879 is the unique solution of the equation log (√ c2 + 1 + c) =√1 + c−2. This bound is optimal. To cite this article: A. Eremenko, P. Yuditskii, C. R. Acad. Sci. Paris, Ser. I 346 (2008). © 2008 Académie des sciences. Publishe...

Conformal Mappings And Entire Functions With Real Zeros

Convolution Operators and Entire Functions with Simple Zeros

Let G(z) be an entire function of order less than 2 that is real for real z with only real zeros. Then we classify certain distribution functions F such that the convolution (G ∗ dF )(z) = ∫∞ −∞ G(z − is) dF (s) of G with the measure dF has only real zeros all of which are simple. This generalizes a method used by Pólya to study the Riemann zeta function.