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 [Formula: see text] in [Formula: see text] coincide with the values of a highly ubiquitous function called the Rademacher symbol for [Formula: see text] . In this article, we replace [Formula: see text] by the triangle group [Formula: see text] for any coprime pair (p, q) of integers with [Formula: see text] . We invoke the theory of harmonic Maass forms for [Formula: see text] to introduce the notion of the Rademacher symbol [Formula: see text] , and provide several characterizations. Among other things, we generalize Ghys’s theorem for modular knots around any “missing” torus knot [Formula: see text] in [Formula: see text] and in a lens space.