ABSTRACT. For entire functions of order zero we introduce a new concept of regularity of growth, which is shown to possess properties similar to those which characterize the concept of totally regular growth of entire functions of finite order in the sense of Levin-Pfliiger.KEY WORDS: entire function of order zero, regularity of growth, function of totally regular growth, function of strongly regular growth. Let n(r, a, fl) be the number of roots of the function f in the sector {z : Izl <_ r, a < argz <_ fl}. We say [1, pp. 118-119] that the set of roots of an entire function has angular density if the limitexists for all a, 1~ with the exception, perhaps, of ~ or fl belonging to some countable set. In this case, for a given a, the relation A(fl) -A(a) = A(a, fl) defines a nondecreasing function A(fl) up to an arbitrary constant. In [1, Chaps. 2 and 3] a complete description of entire functions of totally regular growth is given. In particular, if p is noninteger, then the entire function f is a function of totally regular growth if and only if the set of its roots has angular density; moreover,
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