Masatake Hirao

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

For a finite subset X of the d -dimensional unit sphere, the harmonic strength T ( X ) of X is the set of ℓ ∈ ℕ such that ∑ x ∈ X P ( x ) = 0 for all harmonic polynomials P of homogeneous degree ℓ . We will study three exceptional finite groups of unit quaternions, called the bin...