AbstractIn 1994 Faltings and W\"ustholz introduced a new geometric method in the study of Diophantine approximation, called the filtration method, which involved working with ``many" sections of a line bundle and producing many linear combinations of them vanishing along appropriate divisors. This was further developed by Evertse and Ferretti. Independently, Corvaja and Zannier also worked with...
AbstractIn this talk we discuss a notion of $\psi$-Dirichlet in Diophantine approximation which concerns improving Dirichlet’s approximation theorem to a general approximating function $\psi$. This notion was introduced by Kleinbock and Wadleigh in 2018 and generalizes the classical notion of a matrix being Dirichlet-improvable. In particular, we prove a partial zero-one law for the Lebesgue m...
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