# Mabud Ali SarkarUniversity of Burdwan | B.U. · Department of Mathematics

Mabud Ali Sarkar

Master of Science

My website-
https://sites.google.com/view/mabudalisarkar/home

## About

8

Publications

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Introduction

I am working on Algebraic Number Theory, Arithmetic Geometry, Algebraic Geometry and Formal Group Laws.
Go to this link to know more about my research information-https://sites.google.com/view/mabudalisarkar/home

**Skills and Expertise**

Additional affiliations

March 2018 - present

Education

March 2018 - December 2022

## Publications

Publications (8)

In 1964, Professors Jonathan Lubin and John Tate introduced a 1-dimensional formal group known as Lubin-Tate formal group, and applied its torsion points to provide a parallel interpretation of class field theory by explicitly defining the local reciprocity map. This has several rigorous applications in number theory, algebraic geometry, and algebr...

This paper computes the bases of the image of the 2-adic logarithm on the group of the principal units in all 7 quadratic extensions of Q2. This helps one understand the free module structure of the 2-adic logarithm at arbitrary points on its domain. We discuss some applications at the end.

In this work, we study arithmetic dynamical questions for formal groups and $p$-adic dynamical systems in higher dimensions. As a generalization of Berger's result in 1-dimensional case, in the paper, we prove that for any two higher-dimensional formal groups over the ring of $p$-adic integers, if they have infinitely many torsion points in common,...

Berger asked the question
"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 applied the preperiodic points of a stable p-adic power series in order to determine the corresponding stable p-adic dynamical system.

The $p$-adic logarithm appears in many places in number theory. Hence having a good description of the image of the $p$-adic logarithm could be useful, and in particular, to figure out the image of $1 + \mathfrak{m}_K$, where $K$ is an algebraic extension of $\mathbb{Q}_p$ and $\mathfrak{m}_K$ its maximal ideal. If the ramification index of $K$ is...

Studied properties of breuil-kisin module

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 summation formula which is invariant for rational argument. More precisely, we have investigated a sufficient condition under which the p-adic power series converges to...

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 p-adic norm and real norm under certain conditions. Then we have studied convergence of specially constructed power series and derived summation formula. Finally, we hav...

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