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- W2740184890 abstract "We consider Riemann’s zeta function from the viewpoint of the theory of stationary Gaussian processes. In the previous two papers ([11, 12]), we proved that Riemann’s zeta function satisfies an ordinary differential equation with time delay and then obtained a new representation of the KM2O-Langevin system which is the characteristics for the non-negative definite function associated with Riemann’s zeta function. As a continuation of the previous papers, first, we introduce in this paper a derived Kummer function and prove a new representation theorem for an analytic continuation for Riemann’s zeta function, by obtaining an analytic continuation of the derived Kummer function. Second, we prove an inner product representation theorem for the analytic continuation of Riemann’s zeta function and the derived Kummer function, by constructing a Hamiltonian operator associated with a stationary Gaussian process with T-positivity." @default.
- W2740184890 created "2017-08-08" @default.
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- W2740184890 date "2012-01-01" @default.
- W2740184890 modified "2023-10-17" @default.
- W2740184890 title "Riemann's zeta function and T-positivity (3): Kummer function and inner product representation" @default.
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