Note on an explicit formula of Rademacher symbols for triangle groups

TL;DR

This paper provides an explicit formula for Rademacher symbols associated with triangle groups, extending previous work and linking it to modular knot linking numbers.

Contribution

It introduces a generalized explicit formula for Rademacher symbols for triangle groups, expanding on Ghys' proof and connecting to modular knot theory.

Findings

Explicit formula for Rademacher symbols for triangle groups

Generalization of Ghys' proof of linking number identities

Connection between Rademacher symbols and modular knots

Abstract

The purpose of this note is to present an explicit formula of the Rademacher symbols for triangle groups. This result generalizes Ghys' third proof of the identity relating to the linking numbers of modular knots.