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Solutions of the linear Boltzmann equation and some Dirichlet series
-
Alexander V. Bobylev
and
Irene M. Gamba
Published/Copyright:
February 25, 2012
Abstract.
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 result is based on 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.
Keywords.: Boltzmann equation; Dirichlet series and functional
equations; Riemann Zeta and -functions
Received: 2010-03-20
Published Online: 2012-02-25
Published in Print: 2012-March
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Boltzmann equation;
Dirichlet series and functional
equations;
Riemann Zeta and -functions
Articles in the same Issue
- Masthead
- Uniform weighted estimates for oscillatory singular integrals
- Solutions of the linear Boltzmann equation and some Dirichlet series
- Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
- Periodic flat resolutions and periodicity in group (co)homology
- Precompact noncompact reflexive Abelian groups
-
Free profinite
-
Cellular covers for
- Time changes of local Dirichlet spaces by energy measures of harmonic functions
- A construction of a universal connection
- Finitely generated algebraic structures with various divisibility conditions
- Quasiprojective varieties admitting Zariski dense entire holomorphic curves
- Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms
