Abstract:
After recalling the precise existence conditions of the zeta function of a pseudodifferential operator, and the concept of reflection formula, an exponentially convergent expression for the analytic continuation of a multidimensional inhomogeneous Epstein-type zeta function of the general form
with A the p×p$ matrix of a quadratic form, a p vector and q a constant, is obtained. It is valid on the whole complex s-plane, is exponentially convergent and provides the residua at the poles explicitly. It reduces to the famous formula of Chowla and Selberg in the particular case p=2, , q=0. Some variations of the formula and physical applications are considered.
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Received: 20 July 1997 / Accepted: 27 March 1998
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Elizalde, E. Multidimensional Extension of the Generalized Chowla–Selberg Formula. Comm Math Phys 198, 83–95 (1998). https://doi.org/10.1007/s002200050472
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DOI: https://doi.org/10.1007/s002200050472