Abstract
A complex number w will be called a linearly distributed value of the entire function f(z) if there is a straight line l of the complex plane on which all the solutions of f(z)= w lie. For functions of order less than one the occurrence of such values is completely described by Theorem 1. If f(z) is an entire transcendental function of order less than one, then any two linearly distributed values are distributed on the same line; moreover, the set of such values forms a closed straight line segment (which may reduce to a single point or O) of the complex plane. That the theorem is no longer true for functions of order one is shown by e z for which every value is linearly distributed. This is in fact a characteristic property of the exponential function:
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