Sharper Wiman inequality for entire functions with rapidly oscillating coefficients

AbstractFor entire functions of the form ∑∞n = 0aneiθntzn where the θn are integers satisfying the Hadamard gap condition it is proved that Wiman's inequality can be improved to M(r) ⩽ μ(r) (log μ(r))14 (log log μ(r))1 + δ, for almost every t and all r except a set Eδ(t) of finite logarithmic measure