Hasse-Weil zeta functions of SL_2-character varieties of arithmetic two bridge link complements

TL;DR

This paper computes the Hasse-Weil zeta functions for SL_2-character varieties of certain arithmetic two-bridge link groups and explores their special values at specific points.

Contribution

It provides explicit calculations of zeta functions for these varieties and analyzes their special values, advancing understanding of their arithmetic properties.

Findings

Explicit formulas for Hasse-Weil zeta functions of the varieties.

Identification of special values at s=0,1,2.

Insights into the arithmetic structure of two-bridge link complements.

Abstract

Hasse-Weil zeta functions of SL_2-character varieties of arithmetic two bridge link groups are determined. Special values of the zeta functions at s=0,1,2 are also investigated.