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
Abstract
Abstract We consider a discrete analogue of the well‐known Littlewood conjecture on Diophantine approximations and obtain a strong upper bound for the number of exceptional vectors in this conjecture.