The monodromy conjecture for plane meromorphic germs

• Verfasst von: González Villa, Manuel [VerfasserIn]
• Verfasst von: Lemahieu, Ann [VerfasserIn]
• Titel: The monodromy conjecture for plane meromorphic germs
• Verf.angabe: Manuel González Villa and Ann Lemahieu
• E-Jahr: 2014
• Jahr: 1 February 2014
• Umfang: 13 S.
• Fussnoten: Gesehen am 18.08.2020
• Titel Quelle: Enthalten in: London Mathematical SocietyBulletin of the London Mathematical Society
• Ort Quelle: Hoboken, NJ : Wiley, 1969
• Jahr Quelle: 2014
• Band/Heft Quelle: 46(2014), 3, Seite 441-453
• ISSN Quelle: 1469-2120
• DOI: doi:10.1112/blms/bdt098
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1727308964

Abstract

A notion of Milnor fibration for meromorphic functions and the corresponding concepts of monodromy and monodromy zeta function have been introduced by Gusein-Zade, Luengo and Melle-Hernández [‘Zeta functions for germs of meromorphic functions, and Newton diagrams’, Funct. Anal. Appl. 32 (1998)]. In this article, we define the topological zeta function for meromorphic germs and we study its poles in the plane case. We show that the poles do not behave as in the holomorphic case but still do satisfy a generalization of the monodromy conjecture.