2022/01/25 by Shantanu Chakrabartty, Chakrabartty, Shantanu
Mathematics · Physics and Astronomy · #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2202.01064
openalex publication_date 2022/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We first construct a dynamical systems model which in its steady-state serves as an analytic continuation of the completed Riemann zeta function over the entire critical strip. The resulting mathematical construct involves a linear interpolation of two symmetric generator functions which can be used to infer the global properties of the non-trivial zeros of the Riemann zeta function using concentration bounds. The proposed dynamical systems framework thus provides an alternative method for investigating the celebrated Riemann Hypothesis which is shown in this paper to be almost surely true. We also show that the framework is general enough to study the non-trivial zeros of the Dirichlet L-functions and in this paper we show that under specific conditions, the generalized Riemann Hypothesis is also almost surely true.