By analogy to Pellikaan's construction, we define the two-variable motivic zeta function of a K-curve X as a power series in two variables over the Grothendieck ring of K-varieties (in terms of the class of the Picard variety of degree n line bundles on X). We also study the properties of the specialization of this construction via motivic measures, and obtain results analogous to those of Pellikaan (see Theorem 1.1 and Theorem 1.2), such as rationality, functional equations, etc.
A motivic version of Pellikaan's two variable zeta function
BALDASSARRI, FRANCESCO;
2007
Abstract
By analogy to Pellikaan's construction, we define the two-variable motivic zeta function of a K-curve X as a power series in two variables over the Grothendieck ring of K-varieties (in terms of the class of the Picard variety of degree n line bundles on X). We also study the properties of the specialization of this construction via motivic measures, and obtain results analogous to those of Pellikaan (see Theorem 1.1 and Theorem 1.2), such as rationality, functional equations, etc.
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