Speiser’s Theorem on the Road

Abstract

In this note we discuss the Gauss-Lucas theorem (for the zeros of the derivative of a polynomial) and Speiser’s equivalent for the Riemann hypothesis (about the location of zeros of the Riemann zeta-function). We indicate similarities between these results and present there analogues in the context of elliptic curves, regular graphs, and finite Euler products.

Keywords

• Riemann zeta-function
• elliptic curve
• Riemann hypothesis
• Speiser’s Theorem
• regular graphs
• Gauss-Lucas theorem