naa a22 4500 510760910 CHVBK 20180411083139.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1007/s13163-012-0101-3 doi (NATIONALLICENCE)springer-10.1007/s13163-012-0101-3 Bories Bart Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001, Leuven, Belgium aut Zeta functions and Bernstein-Sato polynomials for ideals in dimension two [Elektronische Daten] [Bart Bories] For a nonzero ideal $\mathcal {I}\lhd \mathbf {C}[x_{1},\ldots,x_{n}]$ , with $0\in \operatorname {supp}\mathcal {I}$ , a generalization of a conjecture of Igusa-Denef-Loeser predicts that every pole of its topological zeta function is a root of its Bernstein-Sato polynomial. However, typically only a few roots are obtained this way. Following ideas of Veys (Adv. Math. 213(1):341-357, 2007), we study the following question. Is it possible to find a collection $\mathcal{G}$ of polynomials g∈C[x 1, ,x n ], such that, for all $g\in\mathcal{G}$ , every pole of the topological zeta function associated to $\mathcal {I}$ and the volume form gdx 1∧⋯∧dx n on the affine n-space, is a root of the Bernstein-Sato polynomial of $\mathcal {I}$ , and such that all roots are realized in this way. We obtain a negative answer to this question, providing counterexamples for monomial and principal ideals in dimension two, and give a partial positive result as well. Revista Matemática Complutense, 2012 Topological zeta function nationallicence Bernstein-Sato polynomial nationallicence Monodromy conjecture nationallicence Monomial ideal nationallicence Revista Matemática Complutense Springer Milan 26/2(2013-07-01), 753-772 1139-1138 26:2<753 2013 26 13163 https://doi.org/10.1007/s13163-012-0101-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13163-012-0101-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bories Bart Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001, Leuven, Belgium aut NATIONALLICENCE 773 0- Revista Matemática Complutense Springer Milan 26/2(2013-07-01), 753-772 1139-1138 26:2<753 2013 26 13163 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer