A vanishing result for Igusa's p-adic zeta functions with character
Segers, Dirk
Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, p. 735-754 / Harvested from Project Euclid
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Let $K$ be a $p$-adic field and let $f$ be a $K$-analytic function on an open and compact subset of $K^3$. Let $R$ be the valuation ring of $K$ and let $\chi$ be an arbitrary character of $R^{\times}$. Let $Z_{f,\chi}(s)$ be Igusa's $p$-adic zeta function. In this paper, we prove a vanishing result for candidate poles of $Z_{f,\chi}(s)$. This result implies that $Z_{f,\chi}(s)$ has no pole with real part less than $-1$ if $f$ has no point of multiplicity 2.
Publié le : 2007-11-14
Classification:  Igusa's $p$-adic zeta function,  11D79,  11S80,  14B05,  14E15 
@article{1195157141,
     author = {Segers, Dirk},
     title = {A vanishing result for Igusa's p-adic zeta functions with character},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {13},
     number = {5},
     year = {2007},
     pages = { 735-754},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1195157141}
}

Segers, Dirk. A vanishing result for Igusa's p-adic zeta functions with character. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp.  735-754. http://gdmltest.u-ga.fr/item/1195157141/