Distance between a Maximum Modulus Point and Zero Set of an Entire Function
Iossif Vladimirovich Ostrovskii, Adem Ersin Üreyen · Complex Variables Theory and Application An International Journal · 2003
Let f be an entire function of finite positive order. A maximum modulus point is a point w such that |f(w)|= max {|f(z)|:|z=|w|}. We obtain lower bounds for the distance between a maximum modulus point w and the zero set of f. These bounds are valid for all sufficiently large values of |w|.