On the exceptional set in Littlewood's discrete conjecture | Synapse
April 19, 2026Open Access
On the exceptional set in Littlewood's discrete conjecture
Key Points
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.