Somnath Jha

activity

20152026

most citedControl theorem and functional equation of Selmer groups over

p

-adic Lie extensions

3 citations · 7 across the 16 of their papers we have counts for

collaborators

19 papers

math.AG2026

Combs and complex structures on the six-sphere

Jeff Viaclovsky

We construct complex structures on the six-sphere $S^{6}$ with arbitrarily large local Kuranishi dimension. As a corollary, we find the same phenomenon holds for the smooth manifold…

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

On certain root number $1$ cases of the cube sum problem

Shamik Das, Somnath Jha

We consider certain families of integers $n$ determined by some congruence condition, such that the global root number of the elliptic curve $E_{- 432 n^{2}} : Y^{2} = X^{3} - 432 n^{2}$ is $1$ fo…

math.NT2025

2-Selmer companion modular forms

Abhishek, Somnath Jha, Sudhanshu Shekhar

Let $N$ be a positive integer and $K$ be a number field. Suppose that $f_{1}, f_{2} \in S_{k} (Γ_{0} (N))$ are two newforms such that their residual Galois representations at $2$ are isomorph…

math.NT2025

A $p$ -Converse theorem for Real Quadratic Fields

Muskan Bansal, Somnath Jha, Aprameyo Pal +1

Let $E$ be an elliptic curve defined over a real quadratic field $F$ . Let $p > 5$ be a rational prime that is inert in $F$ and assume that $E$ has split multiplicative reduction at…

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.NT2025★ 1 cited

Asymptotic Fermat equation of signature $(r, r, p)$ over totally real fields

Somnath Jha, Satyabrat Sahoo

Let $K$ be a totally real number field and $O_{K}$ be the ring of integers of $K$ . This manuscript examines the asymptotic solutions of the Fermat equation of signature $(…

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

Iwasawa theory for Rankin-Selberg convolution at an Eisenstein prime

Somnath Jha, Sudhanshu Shekhar, Ravitheja Vangala

Let $p$ be an odd prime, $f$ be a $p$ -ordinary newform of weight $k$ and $h$ be a normalized cuspidal $p$ -ordinary Hecke eigenform of weight $l < k$ . In this article, we…

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

Iwasawa theory of fine Selmer groups over global fields

Sohan Ghosh, Somnath Jha, Sudhanshu Shekhar

The $p^{\infty}$ -fine Selmer group of an elliptic curve $E$ over a number field $F$ is a subgroup of the classical $p^{\infty}$ -Selmer group of $E$ over $F$ . Fine Selmer group is close…

math.NT2020

Twisting lemma for $Λ$ -adic modules

Sohan Ghosh, Somnath Jha, Sudhanshu Shekhar

A classical twisting lemma says that given a finitely generated torsion module $M$ over the Iwasawa algebra $Z_{p} [[Γ]]$ with $Γ ≅ Z_{p}, \exists$ a continuous c…

math.NT2020

Multiplicities in Selmer groups and root numbers for Artin twists

Somnath Jha, Tathagata Mandal, Sudhanshu Shekhar

Let $K / F$ be a finite Galois extension of number fields and $σ$ be an absolutely irreducible, self-dual representation of $Gal (K / F)$ . Let $p$ be an odd prime and consider…

math.NT2019★ 3 cited

Control theorem and functional equation of Selmer groups over $p$ -adic Lie extensions

Somnath Jha, Tadashi Ochiai

Let us consider a $p$ -adic Lie extension of a number field $K$ which fits into the setting of non-commutative Iwasawa theory formulated by Coates-Fukaya-Kato-Sujatha-Venjakob. For…

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★ 2 cited

Non-commutative twisted Euler characteristic

Somnath Jha, Sudhanshu Shekhar

It is well known that given a finitely generated torsion module $M$ over the Iwasawa algebra $Z_{p} [[Γ]]$ , where $Γ ≅ Z_{p}$ , there exists a continuous $p$ -adic char…

math.NT2015★ 1 cited

On twists of modules over non-commutative Iwasawa algebras

Somnath Jha, Tadashi Ochiai, Gergely Zábrádi

It is well known that, for any finitely generated torsion module M over the Iwasawa algebra Z_p [[Γ ]], where Γ is isomorphic to Z_p, there exists a continuous p-adic character ρ o…

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…

Combs and complex structures on the six-sphere

Explicit mock Heegner points and BSD formula on certain Mordell curves

On certain root number 1 cases of the cube sum problem

2-Selmer companion modular forms

A p-Converse theorem for Real Quadratic Fields

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

Asymptotic Fermat equation of signature (r,r,p) over totally real fields

Hilbert's 10th Problem via Mordell curves

Binary Cubic Forms and Rational Cube Sum Problem

Iwasawa theory for Rankin-Selberg convolution at an Eisenstein prime

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

Iwasawa theory of fine Selmer groups over global fields

Twisting lemma for Λ-adic modules

Multiplicities in Selmer groups and root numbers for Artin twists

Control theorem and functional equation of Selmer groups over p-adic Lie extensions

pr-Selmer companion modular forms

Non-commutative twisted Euler characteristic

On twists of modules over non-commutative Iwasawa algebras

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

On certain root number $1$ cases of the cube sum problem

A $p$ -Converse theorem for Real Quadratic Fields

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

Asymptotic Fermat equation of signature $(r, r, p)$ over totally real fields

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

Twisting lemma for $Λ$ -adic modules

Control theorem and functional equation of Selmer groups over $p$ -adic Lie extensions

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