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Linear Boltzmann equation and some Dirichlet series

Tuesday 28th September 2010 - 15:00 to 15:45
INI Seminar Room 1
Seminar Series: 
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.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons