4 papers
math.NT2026
A note on exact approximations
Dmitry Gayfulin, Sergei Pitcyn
Based on M. Hall's theorem we prove a simple result dealing with real numbers which admit exact approximations by rationals.
math.NT2025
Sums of Laurent series with bounded partial quotients
Dmitry Gayfulin, Erez Nesharim
In 1947 M.Hall proved that every real number is the sum of an integer and two real numbers whose partial quotients are at most . Later, Cusick proved that every real number is t…
math.NT2025
Every real number is a sum of two real numbers with diverging partial quotients
Dmitry Gayfulin, Erez Nesharim
We show that every irrational number is a sum of two real numbers with diverging partial quotients. The proof is constructive. The key towards these results is an algorithm which w…
math.NT2023
Hausdorff dimension estimates for Sudler products with positive lower bound
Dmitry Gayfulin, Manuel Hauke
Given an irrational number , we study the asymptotic behaviour of the Sudler product denoted by . We show that $\liminf_{N \to \i…