Dipramit Majumdar

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20152026

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9 papers · 1 filter

math.NT2026

Explicit mock Heegner points and BSD formula on certain Mordell curves

Sumita Gunri, Somnath Jha, Dipramit Majumdar

For a natural number $a$ , let $E_{2 a}$ be the Mordell elliptic curve $X^{3} + Y^{3} = 2 a$ . We give an explicit construction of (mock) Heegner point on the Mordell curve $E_{2 p}$ for a pri…

math.NT2025

$- 3$ -Selmer groups, ideal class groups and large $3$ -Selmer ranks

Somnath Jha, Dipramit Majumdar, Pratiksha Shingavekar

We consider the family of elliptic curves $E_{a, b} : y^{2} = x^{3} + a (x - b)^{2}$ with $a, b \in Z$ . These elliptic curves have a rational $3$ -isogeny, say $φ$ . We give an upper and a l…

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}…

math.NT2024

Hilbert's 10th Problem via Mordell curves

Somnath Jha, Debanjana Kundu, Dipramit Majumdar

We show that for $5/6$ -th of all primes $p$ , Hilbert's 10-th Problem is unsolvable for $Q (ζ_{3}, 3 p)$ . We also show that there is an infinite set $S$ of square free…

math.NT2022

Cube sum problem for integers having exactly two distinct prime factors

Dipramit Majumdar, Pratiksha Shingavekar

Given an integer n>1, it is a classical Diophantine problem that whether n can be written as a sum of two rational cubes. The study of this problem, considering several special cas…

math.NT2022

On characteristic ideal of Selmer group associated to Artin representations

Dipramit Majumdar, Subhasis Panda

Selmer group for an Artin representation over totally real fields was studied by Greenberg and Vatsal. In this paper we study the Selmer groups for an Artin representation over a t…