Modular forms and ellipsoidal T-designs
Tóm tắt
In recent work, Miezaki introduced the notion of a spherical T-design in
$$\mathbb {R}^2$$
, where T is a potentially infinite set. As an example, he offered the
$$\mathbb {Z}^2$$
-lattice points with fixed integer norm (a.k.a. shells). These shells are maximal spherical T-designs, where
$$T=\mathbb {Z}^+\setminus 4\mathbb {Z}^+$$
. 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.
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