Coarse equidistribution of the argument of entire functions of finite order

Анотація

Given a sector S Ì C and an entire function f of order r, we estimate from below the relative area of the preimage f ^-1S. We show that there exist arbitrarily large r such that for any sector S of opening a, the relative area of the set {f ^-1S} Ç rD is bounded from below by a × k(r), where k(r) > 0 depends only on r, and k(r) ~ const r^-1 for r →∞.