Regularization of p-adic String Amplitudes, and Multivariate Local Zeta   Functions
  We prove that the p-adic Koba-Nielsen type string amplitudes are bona fide integrals. We attach to these amplitudes Igusa-type integrals depending on several complex parameters and show that these integrals admit meromorphic continuations as rational functions. Then we use these functions to regularize the Koba-Nielsen amplitudes. As far as we know, there is no a similar result for the Archimedean Koba-Nielsen amplitudes. We also discuss the existence of divergencies and the connections with multivariate Igusa's local zeta functions. 
Miriam Bocardo-Gaspar, H. Garc\'ia-Compe\'an, W. A. Z\'u\~niga-Galindo
math-ph math.MP