Mabud Ali Sarkar

activity

20182026

collaborators

10 papers

math.NT2026

On the Image of the $p$ -adic Logarithm on Annuli of Principal Units

Mabud Ali Sarkar

Let $K$ be a finite extension of $Q_{p}$ , and let $m_{K}$ be its maximal ideal. The image of the group of principal units $1 + m_{K}$ under $p$ -adic logarith…

math.NT2023

Constructing $2$ -dimensional Lubin-Tate formal groups over $Z_{p}$ (I)

Ramla Abdellatif, Mabud Ali Sarkar

In this paper, we construct a class of $2$ -dimensional formal groups over $Z_{p}$ that provide a higher-dimensional analogue of the usual $1$ -dimensional Lubin-Tate formal g…

math.NT2023

Unlikely intersection in higher-dimensional formal groups

Ramla Abdellatif, Mabud Ali Sarkar, Absos Ali Shaikh

In this article, we identify a class of higher-dimensional formal groups over the ring of $p$ -adic integers that are uniquely determined by their $p$ -power torsion points. More pre…

math.NT2021

Rigidity and unlikely intersections for stable $p$ -adic dynamical systems

Mabud Ali Sarkar, Absos Ali Shaikh

Berger asked the question \enquote{To what extent the preperiodic points of a stable $p$ -adic power series determines a stable $p$ -adic dynamical system} ? In this work we have app…

math.NT2021

Properties of Breuil-Kisin modules inherited by $p$ -divisible groups

Mabud Ali Sarkar, Absos Ali Shaikh

In this paper, by assuming a faithful action of a finite flat $Z_{p}$ -algebra $R$ on a $p$ -divisible group $G$ defined over the ring of $p$ -adic integers…

math.NT2020

On the freeness and projectiveness of Breuil-Kisin module

Absos Ali Shaikh, Mabud Ali Sarkar

In the work we have considered Breuil-Kisin module over the ring of witt vectors $W (κ)$ over the residue field $κ$ of characteristic $p$ and a finite flat $Z_{p}$ -algebra $R…

math.NT2019

On Rational Invariant Summation of p-Adic Power Series with Binomial Coefficient

Absos Ali Shaikh, Mabud Ali Sarkar

In the work we have considered p-adic functional series with binomial coefficients and discussed its p-adic convergence. Then we have derived a recurrence relation following with a…

math.NT2019

On the bases of the image of $2$ -adic logarithm on the group of principal units

Mabud Ali Sarkar, Absos Ali Shaikh

This paper computes the bases of the image of $2$ -adic logarithm on the group of the principal units in all 7 quadratic extensions of $Q_{2}$ . This helps one to understand t…

math.NT2019

On the image of $p$ -adic logarithm on principal units

Mabud Ali Sarkar, Absos Ali Shaikh

The $p$ -adic logarithm appears in many places in number theory. Therefore, a comprehensive description of the image of the $p$ -adic logarithm would be beneficial. In particular, it…

math.NT2018

On convergence and rational summation of power series in p-adic field

Absos Ali Shaikh, Mabud Ali Sarkar

In this paper we have discussed convergence of power series both in p-adic norm as well as real norm. We have investigated rational summability of power series with respect to both…

On the Image of the p-adic Logarithm on Annuli of Principal Units

Constructing 2-dimensional Lubin-Tate formal groups over Zp​ (I)

Unlikely intersection in higher-dimensional formal groups

Rigidity and unlikely intersections for stable p-adic dynamical systems

Properties of Breuil-Kisin modules inherited by p-divisible groups

On the freeness and projectiveness of Breuil-Kisin module

On Rational Invariant Summation of p-Adic Power Series with Binomial Coefficient

On the bases of the image of 2-adic logarithm on the group of principal units

On the image of p-adic logarithm on principal units

On convergence and rational summation of power series in p-adic field

On the Image of the $p$ -adic Logarithm on Annuli of Principal Units

Constructing $2$ -dimensional Lubin-Tate formal groups over $Z_{p}$ (I)

Rigidity and unlikely intersections for stable $p$ -adic dynamical systems

Properties of Breuil-Kisin modules inherited by $p$ -divisible groups

On the bases of the image of $2$ -adic logarithm on the group of principal units

On the image of $p$ -adic logarithm on principal units