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