Orbifold Zeta Functions for Dual Invertible Polynomials

Abstract

AbstractAn invertible polynomial innvariables is a quasi-homogeneous polynomial consisting ofnmonomials so that the weights of the variables and the quasi-degree are well defined. In the framework of the construction of mirror symmetric orbifold Landau–Ginzburg models, Berglund, Hübsch and Henningson considered a pair (f, G) consisting of an invertible polynomialfand an abelian groupGof its symmetries together with a dual pair. Here we study the reduced orbifold zeta functions of dual pairs (f, G) andand show that they either coincide or are inverse to each other depending on the numbernof variables.