Families of mutually isospectral Riemannian orbifolds

linowitz, benjamin;

In this paper, we consider three arithmetic families of isospectral non-isometric Riemannian orbifolds and in each case derive an upper bound for the size of the family which is polynomial as a function of the volume of the orbifolds. The first family that we consider are those constructed by Vign´eras’ method. The second and third families are those whose covering groups are the minimal covolume arithmetic subgroups and maximal arithmetic subgroups of PGL2(R)a × PGL2(C)b.