Functions of bounded index and their logarithmic derivatives

Some improvements of criteria of $L$-index boundedness in direction

“…As sufficient conditions of boundedness of index or l-index they improve corresponding results of G. H. Fricke (see Theorem 5 in [3] and Theorem 2 in [4]) and M. M. Sheremeta, A. D. Kuzyk (see Theorems 1 and 6 in [5]). …”

“…[3], [4], [5]). We remind some definitions of the theory of entire functions (more details are in [16]).…”

On some problem for entire functions of unbounded index in any direction

“…The following theorem and its analogues for various classes of analytic functions are called the logarithmic criterion (one-dimensional proposition was obtained in [8,12]). Theorem 2 ( [5,7]).…”

Entire Functions of Bounded L-Index: Its Zeros and Behavior of Partial Logarithmic Derivatives

“…For = 1 Theorem 9 implies the following corollary. (1) for every > 0 there exists 1 = 1 ( ) > 0 such that for all ∈ C \ ( ) It is known (see [12,27,29]) that in one-dimensional case conditions (1) and (3) We need some notations from [1]. Let b ∈ C \ {0} be a given direction.…”

“…The different estimates of measure of zero set and its geometrical properties are investigated in [17][18][19][20][21][22]. We suppose that zero points of entire functions admit uniform distribution in some sense, that is, (29).…”