Video library: A. Yu. Popov, Lower bound for the minimum modulus of an entire function of genus zero on a frequent sequence of circles

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International Conference on Complex Analysis Dedicated to the Memory of Andrei Gonchar and Anatoliy Vitushkin November 21, 2023 11:00, Steklov Institute, conference hall, 9th floor

Lower bound for the minimum modulus of an entire function of genus zero on a frequent sequence of circles A. Yu. Popov Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
https://youtu.be/xu3IoWTOrnI Abstract: We consider the class of entire functions of genus zero (as is known, such a class contains all entire functions of order $<1$) with positive roots. It is shown that for any function $f$ from this class and an arbitrary $\delta>0$ there is a sequence $r_n\uparrow+\infty$ such that the sequence of ratios $r_{n+1}/r_n$ is bounded and an estimate from below for the minimum modulus of $f$ on a circle $\|z\|=r_n$ through a negative (equil to $-1-\delta$) power of the maximum modulus of $f$ on the same circle is valid. In the case of small values of the upper limit of the ratios $r_{n+1}/r_n$ estimates for exponent of the maximum modulus that are close to optimal were found. Website: https://zoom.us/j/98008001815?pwd=OG1rTVRFRzFpY3RhZmE4MXFwckxMUT09 ^* ID: 980 0800 1815; Password: 055016