Modular knots, automorphic forms, and the Rademacher symbols for triangle groups

É. Ghys proved that the linking numbers of modular knots and the "missing" trefoil $$ in $$ coincide with the values of a highly ubiquitous function called the Rademacher symbol for $$ . In this article, we replace $$ by the triangle group $$ for any coprime pair (p, q) of integers with $$ . We invoke the theory of harmonic Maass forms for $$ to introduce the notion of the Rademacher symbol $$ , and provide several characterizations. Among other things, we generalize Ghys's theorem for modular knots around any "missing" torus knot $$ in $$ and in a lens space.