T. Hakobyan

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20142018

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math.NT2018

Honda formal group as Galois module in unramified extensions of local fields

Tigran Hakobyan, Sergei Vostokov

For given rational prime number $p$ consider the tower of finite extensions of fields $K_{0} / Q_{p},$ $K / K_{0}, L / K, M / L$ , where $K / K_{0}$ is unramified and $M / L$ is a Galois exten…

math.NT2016

On the $P_{1}$ property of sequences of positive integers

Tigran Hakobyan

It is well-known that for any non-constant polynomial $P$ with integer coefficients the sequence $(P (n))_{n \in N}$ has the property that there are infinitely many prime nu…

math.NT2016

On the unboundedness of common divisors of distinct terms of the sequence $a_{n} = 2^{2^{n}} + d$ for $d > 1$

Tigran Hakobyan

It is well-known that for any distinct positive integers $k$ and $n$ , the numbers $2^{2^{k}} + 1$ and $2^{2^{n}} + 1$ are relatively prime. In this paper we consider the situation when 1 i…

math.NT2014

On an asymptotic behavior of the divisor function $τ (n)$

Tigran Hakobyan

For $μ > 0$ we study an asymptotic behavior of the sequence defined as $T_{n} (μ) = \frac{ma x _{1 \leq m \leq n^{\frac{1}{μ}}} { τ ( n + m )}}{τ ( n )}, n = 1, 2, ...$ where $τ (n)$ denotes the n…

Honda formal group as Galois module in unramified extensions of local fields

On the P1​ property of sequences of positive integers

On the unboundedness of common divisors of distinct terms of the sequence an​=22n+d for d>1

On an asymptotic behavior of the divisor function τ(n)

On the $P_{1}$ property of sequences of positive integers

On the unboundedness of common divisors of distinct terms of the sequence $a_{n} = 2^{2^{n}} + d$ for $d > 1$

On an asymptotic behavior of the divisor function $τ (n)$