ENTIRE DIRICHLET SERIES AND h − MEASURE OF EXCEPTIONAL SETS - Скасків, Олег Богданович; Сало, Тетяна Михайлівна (PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, 2019)
For entire Dirichlet series F(z) =_n=0^+∞ a_ne^zλ_n, 0λ_n +∞ (n→+∞) , we establish necessary conditions for the relation {|F(x+iy)|: y R}= (1+o(1)) {|a_n| e^xλ_n: n 0}to hold when x→+∞ outside some set E such that _E dh (x) <+∞, where h is positive continuous function increasing to +∞ on [0;+∞) with non-increasing derivative.