Ayan Nath

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20212026

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math.NT2024

The moments of split greatest common divisors

Abhishek Jha, Ayan Nath, Emanuele Tron

Sequences of the form $(g cd (u_{n}, v_{n}))_{n \in N}$ , with $(u_{n})_{n}$ , $(v_{n})_{n}$ sums of $S$ -units, have been considered by several authors. The study of $g cd (n, u_{n})$ correspo…

math.NT2022

The Distribution of G.C.D.s of Shifted Primes and Lucas Sequences

Abhishek Jha, Ayan Nath

Let $(u_{n})_{n \geq 0}$ be a nondegenerate Lucas sequence and $g_{u} (n)$ be the arithmetic function defined by $g cd (n, u_{n}) .$ Recent studies have investigated the distributional chara…

math.NT2021

On Quotients of Values of Euler's Function on Factorials

Ayan Nath, Abhishek Jha

Recently, there has been some interest in values of arithmetical functions on members of special sequences, such as Euler's totient function $ϕ$ on factorials, linear recurrences,…

math.NT2021

On the Least Common Multiple of Polynomial Sequences at Prime Arguments

Ayan Nath, Abhishek Jha

Cilleruelo conjectured that if $f \in Z [x]$ is an irreducible polynomial of degree $d \geq 2$ then, $lo g lcm {f (n) ∣ n < x} \sim (d - 1) x lo g x .$ In this artic…