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arXiv · 2004.04298

Modular forms and ellipsoidal T-designs

Badri Vishal Pandey
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Abstract

In recent work, Miezaki introduced the notion of a $spherical$ $T$-d$esign$ 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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Badri Vishal Pandey. 2020-04-08. Modular forms and ellipsoidal T-designs. https://arxiv.org/abs/2004.04298

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