Modular forms and ellipsoidal T-designs

2020/04/08 by Badri Vishal Pandey, Pandey, Badri Vishal · 1 citation
Computer Science · Materials Science · Mathematics · #Digital Image Processing Techniques #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2004.04298

openalex publication_date 2020/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In recent work, Miezaki introduced the notion of a spherical T-design in ℝ², where T is a potentially infinite set. As an example, he offered the ℤ²-lattice points with fixed integer norm (a.k.a. shells). These shells are maximal spherical T-designs, where T=ℤ⁺∖ 4ℤ⁺. 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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