Dipramit Majumdar

activity

20132026

most citedCyclic Cubic Extensions of Q

3 citations · 5 across the 16 of their papers we have counts for

collaborators

18 papers

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.NT2023

Binary Cubic Forms and Rational Cube Sum Problem

Somnath Jha, Dipramit Majumdar, B. Sury

In this note, we use integral binary cubic forms to study the rational cube sum problem. We prove (unconditionally) that for any positive integer $d$ , infinitely many primes in eac…

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

$3$ -Selmer group, ideal class groups and cube sum problem

Somnath Jha, Dipramit Majumdar, Pratiksha Shingavekar

Consider a Mordell curve $E_{a} : y^{2} = x^{3} + a$ with $a \in Z$ . These curves have a rational $3$ -isogeny, say $φ$ . We give an upper and a lower bound on the rank of the $φ$ -Selmer…

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…

math.NT2021

Cuspidal subgroups associated with non-rational Eisenstein maximal ideals

Debargha Banerjee, Narasimha Kumar, Dipramit Majumdar

In this paper, we are interested in the generalization of Ramanujan-like Eisenstein congruences (congruences between cusp forms and Eisenstein series) for congruence subgroups of t…

math.HO2021★ 1 cited

Fruit Diophantine Equation

Dipramit Majumdar, B. Sury

We show that the Diophantine equation given by X^3+ XYZ = Y^2+Z^2+5 has no integral solution. As a consequence, we show that the family of elliptic curve given by the Weierstrass e…

math.NT2021★ 3 cited

Cyclic Cubic Extensions of Q

Dipramit Majumdar, B. Sury

In this article we explicitly describe irreducible trinomials X^3-aX+b which gives all the cyclic cubic extensions of Q. In doing so, we construct all integral points (x,y,z) with…

math.NT2018

A generalization of Mazur's theorem (Ogg's conjecture) for number fields

Debargha Banerjee, Narasimha Kumar, Dipramit Majumdar

In this article, we prove a generalization of a theorem (Ogg's conjecture) due to Bary Mazur for arbitrary $N \in N$ and for {\it number fields}. The main new observation is a modi…

math.NT2018

$p^{r}$ -Selmer companion modular forms

Somnath Jha, Dipramit Majumdar, Sudhanshu Shekhar

The study of $n$ -Selmer group of elliptic curve over number field in recent past has led to the discovery of some deep results in the arithmetic of elliptic curves. Given two ellip…

math.NT2017

p-adic Asai transfer

Baskar Balasubramanyam, Dipramit Majumdar

Let $K / Q$ be a real quadratic field. Given an automorphic representation $π$ for $G L_{2} / K$ , let $A s^{\pm} (π)$ denote the plus/minus Asai transfer of $π$ to an automorphic represen…

math.NT2015

Functional equation for the Selmer group of nearly ordinary Hida deformation of Hilbert modular forms

Somnath Jha, Dipramit Majumdar

We establish a duality result proving the `functional equation' of the characteristic ideal of the Selmer group associated to a nearly ordinary Hilbert modular form over the cyclot…

math.NT2014

Endoscopic transfer between eigenvarieties for definite unitary groups

Dipramit Majumdar

In this paper, we extend the endoscopic transfer of definite unitary group U(n), which sends a pair of automorphic forms of U(m),U(n) to an automorphic form of U(m+n), to finite sl…

math.NT2014★ 1 cited

l-Class groups of cyclic extensions of prime degree l

Manisha Kulkarni, Dipramit Majumdar, Balasubramanian Sury

Let K/F be a cyclic extension of prime degree l over a number field F. If F has class number coprime to l, we study the structure of the l-Sylow subgroup of the class group of K. I…

math.NT2013

Geometry of the eigencurve at critical Eisenstein series of weight 2

Dipramit Majumdar

In this paper we show that the critical Eisenstein series of weight 2, E_{2}^{crit_{p}}, is smooth in the eigencurve C(l), where l is a prime. We also show that E_{2}^{crit_{p},ord…

Explicit mock Heegner points and BSD formula on certain Mordell curves

−3​-Selmer groups, ideal class groups and large 3-Selmer ranks

Relative p-class groups and p-Selmer groups

Hilbert's 10th Problem via Mordell curves

Binary Cubic Forms and Rational Cube Sum Problem

Cube sum problem for integers having exactly two distinct prime factors

3-Selmer group, ideal class groups and cube sum problem

On characteristic ideal of Selmer group associated to Artin representations

Cuspidal subgroups associated with non-rational Eisenstein maximal ideals

Fruit Diophantine Equation

Cyclic Cubic Extensions of Q

A generalization of Mazur's theorem (Ogg's conjecture) for number fields

pr-Selmer companion modular forms

p-adic Asai transfer

Functional equation for the Selmer group of nearly ordinary Hida deformation of Hilbert modular forms

Endoscopic transfer between eigenvarieties for definite unitary groups

l-Class groups of cyclic extensions of prime degree l

Geometry of the eigencurve at critical Eisenstein series of weight 2

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

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

$3$ -Selmer group, ideal class groups and cube sum problem

$p^{r}$ -Selmer companion modular forms