5 papers
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…
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…
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…
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…