Modular forms and ellipsoidal T-designs.

In recent work, Miezaki introduced the notion of a sphericalT-design in R 2 , where T is a potentially infinite set. As an example, he offered the Z 2 -lattice points with fixed integer norm (a.k.a. shells). These shells are maximal spherical T-designs, where T = Z + \ 4 Z + . We generalize the notion of a spherical T-design to special ellipses, and extend Miezaki's work to the norm form shells for rings of integers of imaginary quadratic fields with class number 1. [ABSTRACT FROM AUTHOR]