Masatake Hirao

activity

20112025

most citedFinite frames, frame potentials and determinantal point processes on the sphere

3 citations · 3 across the 4 of their papers we have counts for

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3 papers · 1 filter

math.CO2025

Spherical designs for finite quaternionic unit groups and their applications to modular forms

Masatake Hirao, Hiroshi Nozaki, Koji Tasaka

For a finite subset $X$ of the $d$ -dimensional unit sphere, the harmonic strength $T (X)$ of $X$ is the set of $ℓ \in N$ such that $\sum_{x \in X} P (x) = 0$ for all harmonic…

math.CO2025

More on the corner-vector construction for spherical designs

Kenji Tanino, Tomoki Tamaru, Masatake Hirao +1

This paper explores a full generalization of the classical corner-vector method for constructing weighted spherical designs, which we call the {\it generalized corner-vector method…

math.CO2023

Spherical designs and modular forms of the $D_{4}$ lattice

Masatake Hirao, Hiroshi Nozaki, Koji Tasaka

In this paper, we study shells of the $D_{4}$ lattice with a {slight generalization} of spherical $t$ -designs due to Delsarte-Goethals-Seidel, namely, the spherical design of harmoni…

Spherical designs for finite quaternionic unit groups and their applications to modular forms

More on the corner-vector construction for spherical designs

Spherical designs and modular forms of the D4​ lattice

Spherical designs and modular forms of the $D_{4}$ lattice