Determinant of the Laplacian on Tori of Constant Positive Curvature with one Conical Point

Abstract

We find an explicit expression for the zeta-regularized determinant of (the Friedrichs extensions of) the Laplacians on a compact Riemann surface of genus one with conformal metric of curvature $1$ having a single conical singularity of angle $4\unicode[STIX]{x1D70B}$ .