A Reformulation of the Xi Function

Abstract

This paper proposes a reformulation of the Riemann Xi function in order to investigate its properties. The reformulated function, which depicts the Xi function as the weighted sum of incomplete gamma functions, is validated, and a number of properties are established. These properties are then used to analyze the intersection of the real and imaginary zero level curves. It is shown that a pair of zeros off the critical line is not consistent with these properties, thus validating the Riemann hypothesis.