The asymptotic behaviour of certain entire functions of order zero

Summary A certain class of entire functionsF(s) of order zero which are asymptotically equal to the sum of just two neighbouring terms of their power series when |s| with |args| < – for any fixed > 0, is investigated. Which two terms one has to take, depends upons. It is shown that these functions have infinitely many negative zeros, and the asymptotic behaviour of the zeros is also determined.     

Maximum modulus points and zero sets of entire functions of regular growth

We obtain lower asymptotic at ∞ estimates of the distance between a maximum modulus point and zero set of an entire function provided that the function is of regular growth with respect to a proximate order. The more regular the growth is the better the estimates are, and they are sharp in some sense. The case of infinite order is also considered; in this case a suitable analogue of usual proximate order is exploited. To cite this article: I. Ostrovskii, E. Üreyen, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

On entire functions with zero as a deficient value

We consider entire functions of finite order for which zero is a Nevanlinna deficient value. Estimates are determined for the ratio of the integrated moduli of the logarithmic derivative of the function on a circle of radius r to the Nevanlinna characteristic of the function at r.     

On unique range sets for meromorphic or entire functions

This paper has studied the Gross uniqueness question ignoring multiplicity and relating multiple values, and extended and improved on some related results in [1–8]. Supported in part by National Natural Science Foundation of China     

Strongly regular growth of entire functions of order zero

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-Pflüger. Translated fromMatematicheskie Zameiki, Vol. 63, No. 2, pp. 196–208, February, 1998. This research was partially supported by the International Science Foundation under grant No. UCR000.     

Spectral sets of certain unbounded functions

Summary A. Beurling introduced the concept of spectral sets of unbounded functions to study the possibility of the approximation of those by trigonometric polynomials. We consider spectral sets of unbounded functions in a certain class which contains the square of the Riemann zeta-function as a typical example.