To a given analytic function germ , we associate zeta functions , , defined analogously to the motivic zeta functions of Denef and Loeser. We show that our zeta functions are rational and that they are invariants of the blow-analytic equivalence in the sense of Kuo. Then we use them together with the Fukui invariant to classify the blow-analytic equivalence classes of Brieskorn polynomials of two variables. Except special series of singularities our method classifies as well the blow-analytic equivalence classes of Brieskorn polynomials of three variables.
Soit un germe de fonction analytique. On associe à des fonctions zêta , définies de manière similaire aux fonctions zêta motiviques de Denef et Loeser. On montre que ces fonctions sont rationnelles et ne dépendent que de la classe d’équivalence blow-analytique au sens de Kuo de . En utilisant ces fonctions zêta et l’invariant de Fukui on donne une classification des polynômes de Brieskorn de deux variables à équivalence blow-analytique près. Pour les polynômes de Brieskorn de trois variables on obtient une classification presque complète.
Classification: 14B05, 32S15
Keywords: blow-analytic equivalence, motivic integration, zeta functions, Thom-Sebastiani formulae
@article{AIF_2003__53_7_2061_0, author = {Koike, Satoshi and Parusi\'nski, Adam}, title = {Motivic-type invariants of blow-analytic equivalence}, journal = {Annales de l'Institut Fourier}, pages = {2061--2104}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {7}, year = {2003}, doi = {10.5802/aif.2001}, mrnumber = {2044168}, zbl = {1062.14006}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2001/} }
TY - JOUR TI - Motivic-type invariants of blow-analytic equivalence JO - Annales de l'Institut Fourier PY - 2003 DA - 2003/// SP - 2061 EP - 2104 VL - 53 IS - 7 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2001/ UR - https://www.ams.org/mathscinet-getitem?mr=2044168 UR - https://zbmath.org/?q=an%3A1062.14006 UR - https://doi.org/10.5802/aif.2001 DO - 10.5802/aif.2001 LA - en ID - AIF_2003__53_7_2061_0 ER -
Koike, Satoshi; Parusiński, Adam. Motivic-type invariants of blow-analytic equivalence. Annales de l'Institut Fourier, Volume 53 (2003) no. 7, pp. 2061-2104. doi : 10.5802/aif.2001. https://aif.centre-mersenne.org/articles/10.5802/aif.2001/
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