Igusa local zeta functions of a class of hybrid polynomials

2016/11/07 by Yin, Qiuyu, Hong, Shaofang
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1611.02111

Abstract

In this paper, we study the Igusa's local zeta functions of a class of hybrid polynomials with coefficients in a non-archimedean local field of positive characteristic. Such class of hybrid polynomial was first introduced by Hauser in 2003 to study the resolution of singularities in positive characteristic. We prove the rationality of these local zeta functions and describe explicitly their poles. The proof is based on Igusa's stationary phase formula.

Related

• On Igusa local zeta functions of Hauser hybrid polynomials
• Igusa's local zeta functions of semiquasihomogeneous polynomials
• The Igusa local zeta functions of superelliptic curves
• A New Generating Function for Calculating the Igusa Local Zeta Function
• On the poles of Igusa's Local Zeta Function for algebraic sets