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

Showing 2025Show all

5 papers · 1 filter

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 $(…

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

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