Number Theory

    

A Generalization of the Riemann Functional Equation with Three Variables

Authors: Jose Risomar Sousa

The discovery of a generalization of the Riemann functional equation obtained by exploiting symmetries of a new formula for the Hurwitz zeta function with respect to the shift parameter, $b$, has led to the search for a similar relation for the Lerch $Phi$ function, $Phi(e^z,k,b)$, where a new formula is used as starting point and the symmetries with respect to $b$ are exploited again. To this end, we uncover surprising new ways of producing analytic continuations of finite summations.

Comments: 20 Pages.

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[v1] 2026-08-27 21:31:35

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