Satyabrate Sahoo

activity

20212026

x^{2} = B y^{p} + C z^{p}

and

2 x^{2} = B y^{p} + C z^{p}

over totally real fields

3 citations · 7 across the 13 of their papers we have counts for

collaborators

13 papers

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★ 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.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…

math.NT2024

Generalized Fruit Diophantine equation over number fields

Satyabrat Sahoo, Shanta Laishram

Let $K$ be a number field and $O_{K}$ be the ring of integers of $K$ . In this article, we study the solutions of the generalized fruit Diophantine equation $ax^d-y^2-z^2 +x…

math.NT2024

On the solutions of the generalized Fermat equation over totally real number fields

Satyabrat Sahoo

Let $K$ be a totally real number field and $O_{K}$ be the ring of integers of $K$ . In this article, we study the asymptotic solutions of the generalized Fermat equation $Ax…

math.NT2024★ 3 cited

Asymptotic solutions of the generalized Fermat-type equation of signature $(p, p, 3)$ over totally real number fields

Satyabrat Sahoo, Narasimha Kumar

In this article, we study the asymptotic solutions of the generalized Fermat-type equation of signature $(p, p, 3)$ over totally real number fields $K$ , i.e., $A x^{p} + B y^{p} = C z^{3}$ with p…

math.NT2023

Lehmer-Type bounds and counting rational points of bounded heights on Abelian varieties

Narasimha Kumar, Satyabrat Sahoo

In this article, we study Lehmer-type bounds for the Néron-Tate height of $K ˉ$ -points on abelian varieties $A$ over number fields $K$ . Then, we estimate the number of $K$ -rati…

math.NT2023★ 3 cited

On the solutions of $x^{2} = B y^{p} + C z^{p}$ and $2 x^{2} = B y^{p} + C z^{p}$ over totally real fields

Narasimha Kumar, Satyabrat Sahoo

In this article, we study the solutions of certain type over $K$ of the Diophantine equation $x^{2} = B y^{p} + C z^{p}$ with prime exponent $p$ , where $B$ is an odd integer and $C$ is either…

math.NT2022

On the solutions of $x^{p} + y^{p} = 2^{r} z^{p}$ , $x^{p} + y^{p} = z^{2}$ over totally real fields

Narasimha Kumar, Satyabrat Sahoo

In this article, we study the non-trivial primitive solutions of a certain type for the Diophantine equations $x^{p} + y^{p} = 2^{r} z^{p}$ and $x^{p} + y^{p} = z^{2}$ of prime exponent $p$ , $r \in \math…

math.NT2021

On generation of the coefficient field of a primitive Hilbert modular form by a single Fourier coefficient

Narasimha Kumar, Satyabrat Sahoo

For a primitive Hilbert modular form $f$ over $F$ of weight $k$ , under certain assumptions on image of $ρ ˉ_{f, λ}$ , we calculate the Dirichlet density of primes $p$ fo…

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 Fruit Diophantine equation over number fields

On the solutions of the generalized Fermat equation over totally real number fields

Asymptotic solutions of the generalized Fermat-type equation of signature (p,p,3) over totally real number fields

Lehmer-Type bounds and counting rational points of bounded heights on Abelian varieties

On the solutions of x2=Byp+Czp and 2x2=Byp+Czp over totally real fields

On the solutions of xp+yp=2rzp, xp+yp=z2 over totally real fields

On generation of the coefficient field of a primitive Hilbert modular form by a single Fourier coefficient

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

Asymptotic solutions of the generalized Fermat-type equation of signature $(p, p, 3)$ over totally real number fields

On the solutions of $x^{2} = B y^{p} + C z^{p}$ and $2 x^{2} = B y^{p} + C z^{p}$ over totally real fields

On the solutions of $x^{p} + y^{p} = 2^{r} z^{p}$ , $x^{p} + y^{p} = z^{2}$ over totally real fields