7 papers
On a conjecture of Velani
Sam Chow, Han Yu
We investigate the approximation of elements of the middle-third Cantor set by dyadic rationals, and natural extensions. We prove a conjecture of Velani, completing the metric theo…
Arithmetic regularity as an alternative to transference
Sam Chow, Sean Prendiville, Santiago Vazquez
Since Green (2005), the Fourier-analytic transference principle has dominated the landscape of combinatorial theorems relative to sparse arithmetic sets. We demonstrate a different…
Rational Points in Hyperbolic Regions and Multiplicative Diophantine Approximation on Manifolds
Sam Chow, Rajula Srivastava, Niclas Technau +1
We establish the convergence theory of multiplicative Diophantine approximation for all non-degenerate, smooth manifolds. We also settle said convergence theory for all affine subs…
Simultaneous and multiplicative Diophantine approximation on missing-digit fractals
Sam Chow, Han Yu
We investigate the metric theory of Diophantine approximation on missing-digit fractals. In particular, we establish analogues of Khinchin's theorem and Gallagher's theorem, as wel…
Smooth discrepancy and Littlewood's conjecture
Sam Chow, Niclas Technau
Given , we estimate the smooth discrepancy of the Kronecker sequence . We find that it can be smaller than…
Moment transference principles and multiplicative diophantine approximation on hypersurfaces
Sam Chow, Han Yu
We determine the generic multiplicative approximation rate on a hypersurface. There are four regimes, according to convergence or divergence and curved or flat, and we address all…
Counting rationals and diophantine approximation in missing-digit Cantor sets
Sam Chow, Péter P. Varjú, Han Yu
We establish a new upper bound for the number of rationals up to a given height in a missing-digit set, making progress towards a conjecture of Broderick, Fishman, and Reich. This…