3 papers
math.NT2026
Positive Logarithmic Hausdorff Measures of Exceptional Sets for the -adic and -adic Littlewood Conjectures
Dzmitry Badziahin, Volodymyr Pavlenkov, Evgeniy Zorin
We prove that if the exceptional set for the -adic Littlewood conjecture is non-empty, then its logarithmic Hausdorff dimension is at least one. More precisely, whenever $…
math.NT2026
Rational Points and Brownian Motion
Faustin Adiceam, Volodymyr Pavlenkov, Evgeniy Zorin
Given a real-valued function , let be the number of rational points with denominators at most in the -tubular neighbourhood of the graph of…
math.NT2024
Diophantine approximation and the Mass Transference Principle: incorporating the unbounded setup
Bing Li, Lingmin Liao, Baowei Wnag +2
We develop the Mass Transference Principle for rectangles of Wang \& Wu (Math. Ann. 2021) to incorporate the `unbounded' setup; that is, when along some direction the lower order (…