On the Rubel-Taylor problem on a representation of holomorphic functions (Q5959542)

The author studies a problem of the Rubel-Taylor type and gives conditions under which meromorphic functions on \(\mathbb{C}^n\) are represented by the quotient of two entire functions satisfying a certain kind of growth conditions. The problem of this type was studied by \textit{L. A. Rubel} and \textit{B. A. Taylor} [Bull. Soc. Math. Fr. 96, 53-96 (1968; Zbl 0157.39603)] and \textit{J. Miles} [J. Anal. Math. 25, 371-388 (1972; Zbl 0247.30019)] in the case \(n = 1\). To prove the main result, the author extends the notion of Nevanlinna's characteristic function and introduces a class of meromorphic functions on \(\mathbb{C}^n\) satisfying some growth conditions.