Newton-flow of the Xi-function and Riemann hypothesis

Dirk Lebiedz

Universität Ulm

Tuesday, March 08, 2022, 9:00

HS 1015, Kollegiengebäude I, Platz der Universität 3

The Riemann hypothesis making a statement about the location of the zeros of the Xi-function closely related to the prime number distribution is an open problem since 1859. We suggest approaching it via the Newton-flow, a meromorphic dynamical systems (2-dim. complex-time ODE) of the Xi-function reflecting the zeros location as fixed points in its global phase portrait, which is a ramified Riemann surface. Its backbone is determined by separatrices related to global stability properties. Characterizing separatrices and their asymptotics on the Poincaré sphere compactification might open up a novel view on the Riemann hypothesis. 


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