Index of lacunarity (Q1326907)

The author introduces a notion of the index of lacunarity of a sequence and a set from \(\mathbb{R}\). He gives several results on the connection between the regularity and complete regularity of growth of an entire function, and the lacunarity of its Taylor coefficients and the lacunarity of the set where the function grows. Another result gives an upper estimate of the Valiron defect of a meromorphic function in terms of its Nevanlinna defect and the index of lacunarity of a set on which the Nevanlinna defect is obtained.