Debajyoti De

collaborators

3 papers

math.NT2026

Some Remarks on $I ¨ $ -Congruent Numbers

Shamik Das, Debajyoti De

In this paper, we extend the work of \cite{Chahal} in several directions. We first determine all Heron triangles that tightly circumscribe the unit circle and the associated $I ¨ $ -c…

math.NT2026

$2$ -Selmer groups, $2$ -class groups, and congruent numbers

Shamik Das, Debajyoti De, Sudipa Mondal

In this article, we study necessary conditions for certain square-free integers to be congruent numbers. Our method uses divisibility properties of class numbers of related imagina…

math.NT2024

Relative $p$ -class groups and $p$ -Selmer groups

Debajyoti De, Dipramit Majumdar, Sudipa Mondal

Let $E$ be an elliptic curve with $j$ -invariant $0$ or $1728$ and let $E$ be a $k^{t h}$ twist of $E$ . We show that for any prime $p$ of good reduction of $\widetilde{E}…

Some Remarks on I¨-Congruent Numbers

2-Selmer groups, 2-class groups, and congruent numbers

Relative p-class groups and p-Selmer groups

Some Remarks on $I ¨ $ -Congruent Numbers

$2$ -Selmer groups, $2$ -class groups, and congruent numbers

Relative $p$ -class groups and $p$ -Selmer groups