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math.NT2026
Density of the multidimensional Lagrange spectrum
Dmitry Kleinbock
The Lagrange spectrum is a classical object in number theory, defined as the set of values of where runs through irratio…
math.NT2026
Uniform Diophantine approximation with restrictions via total density of collections of subspaces
Leo Hong, Dmitry Kleinbock, Vasiliy Neckrasov
In 1926 Khintchine introduced a topological argument proving the existence of uncountably many nontrivial singular linear forms of variables. Throughout the years, this…