Sudhanshu Shekhar

activity

20162025

most citedRelating Tate-Shafarevich group of an elliptic curve with class group

8 citations · 16 across the 9 of their papers we have counts for

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10 papers · 1 filter

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.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

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★ 8 cited

Relating Tate-Shafarevich group of an elliptic curve with class group

Dipendra Prasad, Sudhanshu Shekhar

The paper formulates a precise relationship between the Tate-Shafarevich group of an elliptic curve $E$ over $Q$ with a quotient of the classgroup of $Q (E [p])$ …

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.NT2016★ 6 cited

Root numbers and parity of local Iwasawa invariants

Suman Ahmed, Chandrakant Aribam, Sudhanshu Shekhar

Given two elliptic curves $E_{1}$ and $E_{2}$ defined over the field of rational numbers, $Q$ , with good reduction at an odd prime $p$ and equivalent mod $p$ Galois representa…

math.NT2016

Visibility of Shafarevich-Tate group of abelian varieties over number field extensions