Asymptotics of the entire functions with υ-density of zeros along the logarithmic spirals - Zabolotskyj, M.V.; Basiuk, Yu.V. (Carpathian Mathematical Publications, 2019)
Let υ be the growth function such that rυ'(r)/υ (r) → 0 as r → +∞, l_φ^c = {z=te^i(φ+c t), 1 t < +∞} be the logarithmic spiral, f be the entire function of zero order. The asymptotics of f(re^i(θ +c r)) along ordinary logarithmic spirals l_θ^c of the function f with υ-density of zeros along l_φ^c outside the C_0-set is found. The inverse statement is true just in case zeros of f are placed on the finite logarithmic spirals system Γ_m = _j=0^m l_θ_j^c.