Modular forms and ellipsoidal \(T\)-designs (Q2155875)

The paper under review is a nice application of the modular forms, especially theta functions. \textit{T. Miezaki} [Discrete Math. 313, No. 4, 375--380 (2013; Zbl 1259.05030)] defines spherical \(T\)-design in \(\mathbb{R}^2\). In the paper under review, the author extends this result to special ellipses and the norm form shells for rings of integers of imaginary quadratic fields with class number \(1\). Here the shell means \(\mathbb{Z}^2\)-lattice points with fixed integer norm. The proof is based on calculations with the help of theta functions.