On the zeta-function of a polynomial at infinity

1998/01/21 by S. M. Gusein‐Zade, S. M. Gusein-Zade, I. Luengo +5
Mathematics · Physics and Astronomy · #14D25 #14F45 #32S15 #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Equations Stability Results #math.AG #msc:14D25 #msc:14F45 #msc:32S15

paper · pdf · doi:10.48550/arxiv.math/9801093

8 pages, AMSTeX

arxiv created 1998/01/21 · openalex publication_date 1998/01/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the notion of Milnor fibres of the germ of a meromorphic function and the method of partial resolutions for a study of topology of a polynomial map at infinity (mainly for calculation of the zeta-function of a monodromy). It gives effective methods of computation of the zeta-function for a number of cases and a criterium for a value to be atypical at infinity.

Related

• Monodromy zeta functions at infinity, Newton polyhedra and constructible sheaves
• Zeta-functions for germs of meromorphic functions and Newton diagrams
• The monodromy conjecture for plane meromorphic germs
• On atypical values and local monodromies of meromorphic functions
• Monodromy zeta-function of a polynomial on a complete intersection and Newton polyhedra