Aviso: Por labores de mantenimiento y mejora del repositorio, el martes día 1 de Julio, Docta Complutense no estará operativo entre las 9 y las 14 horas. Disculpen las molestias.
 

Zeta-functions for germs of meromorphic functions and Newton diagrams

Loading...
Thumbnail Image

Full text at PDC

Publication date

1998

Advisors (or tutors)

Editors

Journal Title

Journal ISSN

Volume Title

Publisher

Springer Verlag
Citations
Google Scholar

Citation

Abstract

Let f be a meromorphic function germ on (Cn+1, 0); that is, f = P/Q, where P,Q: (Cn+1, 0)! (C, 0) are holomorphic germs. The authors introduce a notion of Milnor fibers and monodromy operators of the germ f around zero and infinity. Based on their previous work [Comment. Math. Helv. 72 (1997), no. 2, 244–256; MR1470090 (98j:32043)] they write down formulas for the zetafunctions of the monodromy operators in terms of partial resolutions of a singularity. In the case where P and Q are non-degenerate relative to their Newton’s diagrams an analog of the formula from [A. N. Varchenko, Invent. Math. 37 (1976), no. 3, 253–262; MR0424806 (54 #12764)] for zeta functions of monodromy operators is obtained. In conclusion, two interesting examples with f = (x3 −xy)/y and f = (xyz +xp +yq +zr)/(xd +yd +zd) are discussed in detail.

Research Projects

Organizational Units

Journal Issue

Description

Keywords

Collections