  Let $f$ be a germ of complex analytic function at $({\mathbf{C}}^{d+1}, 0)$
such that its zero level defines an irreducible germ of quasi-ordinary
hypersurface $(S,0)$. We describe the motivic Igusa zeta function, the motivic
Milnor fibre and the Hodge-Steenbrink spectrum of $f$ at 0 in terms of
topological invariants of the quasi-ordinary hypersurface $(S,0)$.

Algebraic Geometry