Application of Entire Functions in Number Theory

Abstract

As has already been noted, one of the basic motivations for studying entire functions of finite order is that all of the familiar transcendental functions fall into this category (and what is more, for meromorphic functions of finite order, one arrives at the familiar elliptic functions). Thus, by studying the algebraic or arithmetic properties of entire functions of finite order, one implicity studies the algebraic or arithmetic properties of the fundamental transcentental functions. This in turn has a wide variety of applications in transcendental number theory.