A. Jha

activity

20172026

most citedGreatest common divisors of shifted primes and Fibonacci numbers

1 citations · 1 across the 6 of their papers we have counts for

collaborators

7 papers

math.NT2026

The Poisson Tail Conjecture for primes in short intervals

Abhishek Jha

In 1976, Gallagher showed that, conditional on the Hardy--Littlewood conjectures, the number of primes below $x$ in a randomly chosen short interval of length $λ lo g x$ asymptotica…

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

On the greatest common divisor of $n$ and the $n$ th Fibonacci number, II

Abhishek Jha, Carlo Sanna

Let $A$ be the set of all integers of the form $g cd (n, F_{n})$ , where $n$ is a positive integer and $F_{n}$ denotes the $n$ th Fibonacci number. Leonetti and Sanna proved tha…

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.NT2022★ 1 cited

Greatest common divisors of shifted primes and Fibonacci numbers

Abhishek Jha, Carlo Sanna

Let $(F_{n})$ be the sequence of Fibonacci numbers and, for each positive integer $k$ , let $P_{k}$ be the set of primes $p$ such that $g cd (p - 1, F_{p - 1}) = k$ . We prove t…

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,…