Abrarov Dmitry. Description, possible applications of the result on the exact solvability of the Euler-poisson equations in the context of the Langlands program and Matiyasevich graphs of the Riemann zeta function: current state

Natural Sciences / Mathematics / Dynamical systems

Submitted on: Aug 17, 2023, 16:15:33

Description: The Galois functional theory of the Euler-Poisson differential equations is described. It reduces these equations to the S. Kowalevsky case (top) equations, the Painlevé-VI equation, and the equation of an analytical vertical pendulum. The emphasis is on explaining the global exponential and three-dimensional delta-like structure of the general solution of the Euler-Poisson equations, interpreted as a functional rectilinear flow on the canonical functional Klein bottle, and its connection with the analytic functional version of the Langlands duality for simple exceptional Lie groups, the mechanical context of which was discovered by S. Adlaj. These results represent the AntiKAM-theory as further explained and the connection with the Langlands program is highlighted. The possibility of applying the exact solvability of the Euler-Poisson equations to the proof of the Riemann hypothesis and a number of potential technological applications are discussed.

The Library of Congress (USA) reference page : http://lccn.loc.gov/cn2013300046.

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EPELanglandsRiemannHypothesis.pdf