ORBIFOLD ZETA FUNCTIONS FOR DUAL INVERTIBLE POLYNOMIALS

An invertible polynomial in n variables is a quasi-homogeneous polynomial consisting of n monomials 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, Hubsch and Henningson considered a pair (f, G) consisting of an invertible polynomial f and an abelian group G of its symmetries together with a dual pair ((f) over tilde, (G) over tilde). Here we study the reduced orbifold zeta functions of dual pairs (f, G) and ((f) over tilde, (G) over tilde) and show that they either coincide or are inverse to each other depending on the number n of variables.