Satyabrate Sahoo

activity

20232026

most citedAsymptotic Fermat equation of signature

(r, r, p)

over totally real fields

1 citations · 1 across the 6 of their papers we have counts for

collaborators

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10 papers · 1 filter

math.NT2026

Generalized Fermat equation over number fields

Satyabrat Sahoo

Let $K$ be a number field with ring of integers $O_{K}$ , and let $A, B, C \in O_{K} ∖ {0}$ . Denote by $S_{K}^{'}$ the set of prime ideals of $O_{K}$ divid…

math.NT2026

Generalized Fermat equation over cyclotomic $Z_{l}$ -extensions of totally real fields

Satyabrat Sahoo

Let $K$ be a totally real number field of odd degree in which $2$ is inert. Let $l \geq 5$ be a prime with $l ∤ [K : Q]$ and $g cd (\frac{l - 1}{2}, [K : Q]) = 1$ . We…

math.NT2025

A survey on the generalized Fermat equation of various signatures over totally real fields

Satyabrat Sahoo

Following the famous proof of Fermat's Last Theorem by Andrew Wiles using the modularity of elliptic curves over $Q$ , significant developments have been made in the study…

math.NT2025

Effective Generalized Fermat equation of signature $(2 p, 2 q, r)$ with odd narrow class number

Satyabrat Sahoo

Fix a rational prime $r \geq 5$ . In this article, we study the integer solutions of the generalized Fermat equation of signature $(2 p, 2 q, r)$ , namely $x^{2 p} + y^{2 q} = z^{r}$ , where the…

math.NT2025

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.NT2025

Lower bounds for heights on some algebraic dynamical systems

Arnaud Plessis, Satyabrat Sahoo

Let $v$ be a finite place of a number field $K$ and write $K^{n r, v}$ for the maximal field extension of $K$ in which $v$ is unramified. The purpose of this paper is split up into t…

Generalized Fermat equation over number fields

Generalized Fermat equation over cyclotomic Zl​-extensions of totally real fields

A survey on the generalized Fermat equation of various signatures over totally real fields

Effective Generalized Fermat equation of signature (2p,2q,r) with odd narrow class number

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

Lower bounds for heights on some algebraic dynamical systems

Generalized Fermat equation over cyclotomic $Z_{l}$ -extensions of totally real fields

Effective Generalized Fermat equation of signature $(2 p, 2 q, r)$ with odd narrow class number

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