Local zeta functions and Meuser's invariant functions

Motivic integration in all residue field characteristics for Henselian discretely valued fields of characteristic zero

“…Later Pas [26], [27] extended Meuser's result to more general integrals. In view of [18] and [19], it is thus natural to expect that there exists a motivic rational function Z mot (T ) with coefficients in a certain Grothendieck ring such that, for every d ≥ 1, Z d (s) is obtained from Z mot (T ) by a counting procedure and by putting T equal to q −ds .…”

Motivic integration in mixed characteristic with bounded ramification: a summary

“…Later Pas [22], [23] extended Meuser's result to more general integrals. In view of [15] and [16], it is thus natural to expect that there exists some motivic rational function Z mot (T ) with coefficients in some localization of the Grothendieck ring G Fq of definable sets over F q such that, for every d ≥ 1, Z d (s) is obtained from Z mot (T ) by using the morphism G Fq → Z counting rational points over F q d and letting T go to q −ds .…”