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Linear Boltzmann equation and some Dirichlet series

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Partial Differential Equations in Kinetic Theories

It is shown that a broad class of generalized Dirichlet series (including the polylogarithm, related to the Riemann zeta function) can be presented as a class of solutions of the Fourier transformed spatially homogeneous linear Boltzmann equation with a special Maxwell type collision kernel. The proof uses an explicit integral representation of solutions to the Cauchy problem for the Boltzmann equation. Possible applications to the theory of Dirichlet series are briefly discussed. The talk is based on joint paper with Irene Gamba.

This talk is part of the Isaac Newton Institute Seminar Series series.

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