On Barnes beta distributions, Selberg integral and Riemann xi
نویسندگان
چکیده
منابع مشابه
Theory of Barnes Beta distributions
A new family of probability distributions βM,N , M = 0 · · ·N, N ∈ N on the unit interval (0, 1] is defined by the Mellin transform. The Mellin transform of βM,N is characterized in terms of products of ratios of Barnes multiple gamma functions, shown to satisfy a functional equation, and a Shintani-type infinite product factorization. The distribution log βM,N is infinitely divisible. If M < N...
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We apply the Mellin-Barnes integral representation to several situations of interest in mathematical-physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions. These results are then employed in different topics of quantum field theory, which include the high-temperature expansion of the free energy of a scalar field in...
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ژورنال
عنوان ژورنال: Forum Mathematicum
سال: 2016
ISSN: 0933-7741,1435-5337
DOI: 10.1515/forum-2013-0149