Theorem 3.6 (Chang’s Theorem). Assuming that:

  • G a finite abelian group

  • AβŠ†G be of density Ξ±>0

  • Ξ›βŠ‡Spec⁑ρ(πŸ™A) is dissociated

Then |Ξ›|=O(Οβˆ’2logβ‘Ξ±βˆ’1.