Criteria for the regularity of growth of the logarithm of modulus and the argument of an entire function

Abstract

517.53For entire functions whose zero counting functions are slowly increasing, we establish criteria for the regular growth of their logarithms of moduli and arguments in the metric of L p [ , ] 0 2π .

Asymptotic behavior of entire functions of improved regular growth in the metric of $L^p[0, 2\pi]$

“…Similar results for entire functions of zero order whose zero-counting functions are slowly increasing were obtained in [1]. In particular, from [11, Theorem 7.2, p. 78] it follows the following statement.…”