Mabud Ali Sarkar

University of Burdwan | B.U. · Department of Mathematics

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 main objective of this paper is to find out the image of the maximal ideal $m_k=\pi O_k$ of the ring $O_k$ in the finite extension of p-adic logarithmic series induced by formal group law.

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 particularly, we have investigated certain condition so that the p-adic series converges and gives ratio...

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...