M. A. Korolev

collaborators

2 papers

math.NT2024

An upper bound for the second moment of the length of the period of the continued fraction expansion for $d$

M. A. Korolev

If $d$ is not a perfect square, we define $T (d)$ as the length of the minimal period of the simple continued fraction expansion for $d$ . Otherwise, we put $T (d) = 0$ . In the…

math.NT2010

On Karatsuba's Problem Concerning the Divisor Function $τ (n)$

M. A. Korolev

We study an asymptotic behavior of the sum $\sum\limits_{n\le x}\frac{\D τ(n)}{\D τ(n+a)}$. Here $τ (n)$ denotes the number of divisors of $n$ and $a \geq 1$ is a fixed integer.

An upper bound for the second moment of the length of the period of the continued fraction expansion for d​

On Karatsuba's Problem Concerning the Divisor Function τ(n)

An upper bound for the second moment of the length of the period of the continued fraction expansion for $d$

On Karatsuba's Problem Concerning the Divisor Function $τ (n)$