Poles of Archimedean zeta functions for analytic mappings
2012; Wiley; Volume: 87; Issue: 1 Linguagem: Inglês
10.1112/jlms/jds031
ISSN1469-7750
AutoresEdwin León-Cardenal, Willem Veys, W. A. Zúñiga–Galindo,
Tópico(s)advanced mathematical theories
ResumoJournal of the London Mathematical SocietyVolume 87, Issue 1 p. 1-21 Articles Poles of Archimedean zeta functions for analytic mappings E. León-Cardenal, E. León-Cardenal Departamento de Matemáticas- Unidad Querétaro, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Libramiento Norponiente #2000, Fracc. Real de Juriquilla, Santiago de Querétaro, Qro. 76230 , México, [email protected]Search for more papers by this authorWillem Veys, Willem Veys Department of Mathematics, University of Leuven, Celestijnenlaan 200 B, B-3001 Leuven (Heverlee), Belgium, [email protected]Search for more papers by this authorW. A. Zúñiga-Galindo, Corresponding Author W. A. Zúñiga-Galindo [email protected] Departamento de Matemáticas- Unidad Querétaro, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Libramiento Norponiente #2000, Fracc. Real de Juriquilla, Santiago de Querétaro, Qro. 76230 , Mexico[email protected]Search for more papers by this author E. León-Cardenal, E. León-Cardenal Departamento de Matemáticas- Unidad Querétaro, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Libramiento Norponiente #2000, Fracc. Real de Juriquilla, Santiago de Querétaro, Qro. 76230 , México, [email protected]Search for more papers by this authorWillem Veys, Willem Veys Department of Mathematics, University of Leuven, Celestijnenlaan 200 B, B-3001 Leuven (Heverlee), Belgium, [email protected]uven.beSearch for more papers by this authorW. A. Zúñiga-Galindo, Corresponding Author W. A. Zúñiga-Galindo [email protected] Departamento de Matemáticas- Unidad Querétaro, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Libramiento Norponiente #2000, Fracc. Real de Juriquilla, Santiago de Querétaro, Qro. 76230 , Mexico[email protected]Search for more papers by this author First published: 07 August 2012 https://doi.org/10.1112/jlms/jds031Citations: 3 2010 Mathematics Subject Classification 11M41 (primary), 32S05, 14B05, 14M25 (secondary). The third author was partially supported by Conacyt, Grant # 127794. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract Let f=(f1, …, fl):U→Kl, with K=ℝ or ℂ, be a K-analytic mapping defined on an open set U⊂Kn, and let Φ be a smooth function on U with compact support. In this paper, we give a description of the possible poles of the local zeta function attached to (f, Φ) in terms of a log-principalization of the ideal ℐf=(f1, …, fl). When f is a non-degenerate mapping, we give an explicit list for the possible poles of ZΦ(s, f) in terms of the normal vectors to the supporting hyperplanes of a Newton polyhedron attached to f, and some additional vectors (or rays) that appear in the construction of a simplicial conical subdivision of the first orthant. These results extend the corresponding results of Varchenko to the case l⩾1, and K=ℝ or ℂ. In the case l=1 and K=ℝ, Denef and Sargos proved that the candidate poles induced by the extra rays required in the construction of a simplicial conical subdivision can be discarded from the list of candidate poles. We extend the Denef–Sargos result to arbitrary l⩾1. This yields, in general, a much shorter list of candidate poles, which can, moreover, be read off immediately from Γ(f). Citing Literature Volume87, Issue1February 2013Pages 1-21 RelatedInformation
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