My Publications

I am interested in the topological properties of various subsets of p-adic numbers. Currently, I am trying to find conditions which guarantee the denseness of the ratio set of some sets of integers in the set of p-adic numbers. For example, the set of values assumed by homogeneous forms, linear recurrence sequence etc.

Publications

p-Adic quotient sets: Cubic forms, D. Antony, R. Barman, Archiv der Mathematik 118 (2022), pp. 143--149
On denseness of certain direction and generalized direction sets, D. Antony, R. Barman, J. Chattopadhyay, INTEGERS 22 (2022), Article No. 88.
p-Adic quotient sets: Diagonal forms, D. Antony, R. Barman, P. Miska, Archiv der Mathematik 119 (2022), pp. 461--470.
p-Adic quotient sets: linear recurrence sequences , D. Antony, R. Barman, Bulletin of Australian Math. Soc. 108(1) (2023), pp. 19--28.

Preprints

On p-adic denseness of quotients of values of integral forms , D. Antony, R. Barman, S. Gajović.
On the p-adic valuation of third order linear recurrence sequences , D. Antony, R. Barman.
p-Adic quotient sets: linear recurrence sequences with reducible characteristic polynomials , D. Antony, R. Barman.

Projects

Master's project on the topic Representation of convex sets using extreme points under the supervision of Dr. Anjan K. Chakrabarty.