Modular forms and ellipsoidal T-designs

DOI10.1007/S11139-022-00572-6arXiv2004.04298MaRDI QIDQ6338385

Badri Vishal Pandey

Publication date: 8 April 2020

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 $T=mathbb{Z}^{+}setminus4mathbb{Z}^{+}$. 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.

Mathematics Subject Classification ID

Other designs, configurations (05B30) Theta series; Weil representation; theta correspondences (11F27) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11) Class numbers of quadratic and Hermitian forms (11E41)

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