COMPLETE DETERMINATION OF THE SINGULARITY STRUCTURE OF ZETA-FUNCTIONS

Series of extended Epstein type provide examples of non-trivial zeta f unctions with important physical applications. The regular part of the ir analytic continuation is seen to be a convergent or an asymptotic s eries. Their singularity structure is completely determined in terms o f the Wodzicki residue in its generalized form, which is proven to yie ld the residua of all the poles of the zeta function, and not just tha t of the rightmost pole (obtainable from the Dixmier trace). The calcu lation is a very down-to-earth application of these powerful functiona l analytical methods in physics.