Maleeha Khawaja

activity

20222026

most citedTorsion primes for elliptic curves over degree 8 number fields

1 citations · 1 across the 11 of their papers we have counts for

collaborators

11 papers

math.NT2026

On the unit equation $ε + δ = n$ in cubic fields

Maleeha Khawaja, Samir Siksek

Let $n$ be an integer not equal to $- 2$ , $0$ or $2$ . We consider the unit equation $ε + δ = n$ in units $ε, δ$ of cubic fields. We show that this equation has no…

math.NT2026

Primitive points on some low degree Fermat curves

Maleeha Khawaja

Let $n \geq 3$ be an integer. Let $F_{n}$ be the Fermat curve defined by the Fermat equation $x^{n} + y^{n} = z^{n}$ . For a curve $C / Q$ , we say an algebraic point $P\in C(\bar{\mathbb{…

math.NT2025

New Algebraic Points on Curves

Maleeha Khawaja, Samir Siksek

Let $C$ be a smooth projective absolutely irreducible curve of genus at least 2, defined over the rationals. For a number field $L$ , we define the set of $L$ -new points on $C$ to b…

math.NT2024

Conductor exponents for families of hyperelliptic curves

Martin Azon, Mar Curcó-Iranzo, Maleeha Khawaja +2

We compute the conductor exponents at odd places using the machinery of cluster pictures of curves for three infinite families of hyperelliptic curves. These are families of Frey h…

math.NT2024

The modular approach to Diophantine equations over totally real fields

Maleeha Khawaja, Samir Siksek

Wiles' proof of Fermat's last theorem initiated a powerful new approach towards the resolution of certain Diophantine equations over $Q$ . Numerous novel obstacles arise wh…

math.NT2024

A single source theorem for primitive points on curves

Maleeha Khawaja, Samir Siksek

Let $C$ be a curve defined over a number field $K$ and write $g$ for the genus of $C$ and $J$ for the Jacobian of $C$ . Let $n \geq 2$ . We say that an algebraic point $P \in C(\overl…

math.NT2023

Power values of power sums: a survey

Nirvana Coppola, Mar Curcó-Iranzo, Maleeha Khawaja +2

Research on power values of power sums has gained much attention of late, partially due to the explosion of refinements in multiple advanced tools in (computational) Number Theory…

math.NT2023

On perfect powers that are sums of cubes of a nine term arithmetic progression

Nirvana Coppola, Mar Curcó-Iranzo, Maleeha Khawaja +2

We study the equation $(x - 4 r)^{3} + (x - 3 r)^{3} + (x - 2 r)^{3} + (x - r)^{3} + x^{3} + (x + r)^{3} + (x + 2 r)^{3} + (x + 3 r)^{3} + (x + 4 r)^{3} = y^{p}$ , which is a natural continuation of previous works carried out b…

math.NT2023

Primitive algebraic points on curves

Maleeha Khawaja, Samir Siksek

A number field $K$ is primitive if $K$ and $Q$ are the only subextensions of $K$ . Let $C$ be a curve defined over $Q$ . We call an algebraic point $P\in C(\overlin…

math.NT2023★ 1 cited

Torsion primes for elliptic curves over degree 8 number fields

Maleeha Khawaja

Let $d \geq 1$ be an integer and let $p$ be a rational prime. Recall that $p$ is a torsion prime of degree $d$ if there exists an elliptic curve $E$ over a degree $d$ number field $…

math.NT2022

Fermat's Last Theorem over $Q (2, 3)$

Maleeha Khawaja, Frazer Jarvis

In this paper, we begin the study of the Fermat equation $x^{n} + y^{n} = z^{n}$ over real biquadratic fields. In particular, we prove that there are no non-trivial solutions to the Fermat e…

On the unit equation ε+δ=n in cubic fields

Primitive points on some low degree Fermat curves

New Algebraic Points on Curves

Conductor exponents for families of hyperelliptic curves

The modular approach to Diophantine equations over totally real fields

A single source theorem for primitive points on curves

Power values of power sums: a survey

On perfect powers that are sums of cubes of a nine term arithmetic progression

Primitive algebraic points on curves

Torsion primes for elliptic curves over degree 8 number fields

Fermat's Last Theorem over Q(2​,3​)

On the unit equation $ε + δ = n$ in cubic fields

Fermat's Last Theorem over $Q (2, 3)$