A motivic version of Pellikaan's two variable zeta function

TL;DR

This paper introduces a motivic two-variable zeta function for curves over arbitrary fields, extending Pellikaan's finite field results using Kapranov's motivic zeta function concept.

Contribution

It generalizes Pellikaan's two-variable zeta function to a motivic setting over arbitrary fields, broadening its applicability.

Findings

Established a motivic two-variable zeta function for curves over arbitrary fields

Proved generalizations of Pellikaan's results in the motivic context

Extended the concept beyond finite fields

Abstract

Combining the idea of motivic zeta function, due to Kapranov, and Pellikaan's definition of a two- variable zeta function for curves over finite fields in the present note we introduce a motivic two- variable zeta function for curves over arbitrary fields and prove the generalizations of Pellikaan's results in this context.