Zeros of entire functions of finite order

Abstract

Given , , let be the set of all entire functions , with , for which there exists some constant such that . It is shown that the zero set of a function of satisfies and that the union of the zero sets of two functions of is not necessarily the zero set of a function of . Some uniqueness results of Carlson's type are also obtained.

Keywords

• Entire holomorphic functions
• Order of growth
• Zeros