M. R. Gabdullin

collaborators

3 papers

math.CA2023

Trigonometric polynomials with frequencies in the set of cubes

Mikhail R. Gabdullin, Sergei V. Konyagin

We prove that for any $ε > 0$ and any trigonometric polynomial $f$ with frequencies in the set ${n^{3} : N \leq n \leq N + N^{2/3 - ε}}$ , one has $∥ f ∥_{4} ≪ ε^{- 1/4} ∥ f ∥_{2}$ with imp…

math.NT2023

Karatsuba's divisor problem and related questions

Mikhail R. Gabdullin, Vitalii V. Iudelevich, Sergei V. Konyagin

We prove that $p \leq x \sum \frac{1}{τ ( p - 1 )} ≍ \frac{x}{( lo g x ) ^{3/2}}, n \leq x \sum \frac{1}{τ ( n ^{2} + 1 )} ≍ \frac{x}{( lo g x ) ^{1/2}},$ where $τ(n)=\s…

math.NT2022

Prime avoiding numbers is a basis of order $2$

Mikhail R. Gabdullin

For a positive integer $n$ , we denote by $F (n)$ the distance from $n$ to the nearest prime number. We prove that every sufficiently large positive integer $N$ can be represented as…

Trigonometric polynomials with frequencies in the set of cubes

Karatsuba's divisor problem and related questions

Prime avoiding numbers is a basis of order 2

Prime avoiding numbers is a basis of order $2$