We associate with an infinite cyclic cover of a punctured neighborhood of a simple normal crossing divisor on a complex quasi-projective manifold (assuming certain finiteness conditions are satisfied) a motivic zeta function and a motivic infinite cyclic cover and show its birational invariance. Our constructions generalize the notions of motivic zeta function and motivic Milnor fibre of a complex hypersurface singularity germ due to Denef and Loeser.

Coauthors: Anatoly Libgober and Laurentiu Maxim