On the exceptional set in Littlewood's discrete conjecture

Puntos clave

• The aim is to explore the discrete version of Littlewood's conjecture, focusing on exceptional vectors.
• Examine properties of Diophantine approximations in a discrete setting
• Develop theoretical bounds for exceptional vectors
• Establish a strong upper bound for the number of exceptional vectors
• Provide insights into the scope of Littlewood's conjecture in discrete contexts