Jiahui Liang

Spectral Sets Tile in Cyclic Groups of Square-Free Order

We prove the spectral-to-tiling implication in every finite cyclic group of square-free order. The main ingredient is an unconditional prime-step descent theorem. Let q ≥ 3 be prime, let (q, H) = 1, and let (A, Λ) be an m-point spectral pair in ZqH. If q ∤ m, then the reductions...

Spectral Sets Tile in Cyclic Groups of Square-Free Order

We prove the spectral-to-tiling implication in every finite cyclic group of square-free order. The main ingredient is an unconditional prime-step descent theorem. Let q ≥ 3 be prime, let (q, H) = 1, and let (A, Λ) be an m-point spectral pair in ZqH. If q ∤ m, then the reductions...