This work is an answer to a problem posed by N. Kurokawa and H. Ochiai concerning the natural boundary of meromorphy of a multivariate Euler product of Igusa type. More generally, we introduce and determine the maximal domain of meromorphy of a class of multivariate non-uniform Euler products.
This article is the result of a work that the author has done during his thesis. The author wants particularly to thank his advisor Driss Essouabri for his relevant remarks and his careful reading of this paper. He also expresses his gratitude towards Ben Lichtin for his precious advice. He would also like to thank the referees of this paper for their pertinent comments that have improved the presentation of this paper and the Max-Planck Institute for Mathematics of Bonn where he completed the preparation of the manuscript.
© 2015 by De Gruyter