N. Shulga

collaborators

2 papers

math.NT2026

Dirichlet improvability in $L_{p}$ -norms

Nikolay Moshchevitin, Nikita Shulga

For a norm $F$ on $R^{2}$ , we consider the set of $F$ -Dirichlet improvable numbers $DI_{F}$ . In the most important case of $F$ being an $L_{p}$ -norm with $p = \infty$ , wh…

math.NT2025

On a Conjecture of Cusick on a sum of Cantor sets

Nikita Shulga

In 1971 Cusick proved that every real number $x \in [0, 1]$ can be expressed as a sum of two continued fractions with no partial quotients equal to $1$ . In other words, if we define a…

Dirichlet improvability in Lp​-norms

On a Conjecture of Cusick on a sum of Cantor sets

Dirichlet improvability in $L_{p}$ -norms