Multidimensional extension of the generalized Chowla-Selberg formula
Elizalde, E · CERN Document Server (European Organization for Nuclear Research) · 1998
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 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 $p=2$, $\\vec{b}= \\vec{0}$, $q=0$. Some variations of the formula and physical applications are considered.