Deepa Antony

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20212024

most cited

p

-Adic quotient sets: linear recurrence sequences

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

collaborators

7 papers

math.NT2024

$p$ -Adic quotient sets: linear recurrence sequences with reducible characteristic polynomials

Deepa Antony, Rupam Barman

Let $(x_{n})_{n \geq 0}$ be a linear recurrence sequence of order $k \geq 2$ satisfying $x_{n} = a_{1} x_{n - 1} + a_{2} x_{n - 2} + \dots + a_{k} x_{n - k}$ for all integers $n \geq k$ , where $a_1,\dots,a_k,x_…

math.NT2024

On the $p$ -adic valuation of third order linear recurrence sequences

Deepa Antony, Rupam Barman

In a recent paper, Bilu et al. studied a conjecture of Marques and Lengyel on the $p$ -adic valuation of the Tribonacci sequence. In this article, we study the $p$ -adic valuation of…

math.NT2023

On $p$ -adic denseness of quotients of values of integral forms

Deepa Antony, Rupam Barman, Stevan Gajović +1

Given $A \subseteq Z$ , the ratio set or the quotient set of $A$ is defined by $R (A) := {a / b : a, b \in A, b \neq = 0}$ . It is an open problem to study the denseness of $R (A)$ in the $p$ …

math.NT2022★ 1 cited

$p$ -Adic quotient sets: linear recurrence sequences

Deepa Antony, Rupam Barman

Let $(x_{n})_{n \geq 0}$ be a linear recurrence of order $k \geq 2$ satisfying $x_{n} = a_{1} x_{n - 1} + a_{2} x_{n - 2} + \dots + a_{k} x_{n - k}$ for all integers $n \geq k$ , where $a_1,\dots,a_k,x_0,\dots,…

math.NT2022

On denseness of certain direction and generalized direction sets

Deepa Antony, Rupam Barman, Jaitra Chattopadhyay

Direction sets, recently introduced by Leonetti and Sanna, are generalization of ratio sets of subsets of positive integers. In this article, we generalize the notion of direction…

math.NT2022

$p$ -Adic quotient sets: diagonal forms

Deepa Antony, Rupam Barman, Piotr Miska

For a set of integers $A$ , we consider $R (A) = {a / b : a, b \in A, b \neq = 0}$ . It is an open problem to study the denseness of $R (A)$ in the $p$ -adic numbers when $A$ is the set of non…

math.NT2021

$p$ -adic quotient sets: Cubic forms

Deepa Antony, Rupam Barman

For $A \subseteq {1, 2, \dots}$ , we consider $R (A) = {a / b : a, b \in A}$ . It is an open problem to study the denseness of $R (A)$ in the $p$ -adic numbers when $A$ is the set of nonz…

p-Adic quotient sets: linear recurrence sequences with reducible characteristic polynomials

On the p-adic valuation of third order linear recurrence sequences

On p-adic denseness of quotients of values of integral forms

p-Adic quotient sets: linear recurrence sequences

On denseness of certain direction and generalized direction sets

p-Adic quotient sets: diagonal forms

p-adic quotient sets: Cubic forms

$p$ -Adic quotient sets: linear recurrence sequences with reducible characteristic polynomials

On the $p$ -adic valuation of third order linear recurrence sequences

On $p$ -adic denseness of quotients of values of integral forms

$p$ -Adic quotient sets: linear recurrence sequences

$p$ -Adic quotient sets: diagonal forms

$p$ -adic quotient sets: Cubic forms