Samir Siksek

activity

20232026

collaborators

5 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.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

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

Perfect powers in elliptic divisibility sequences

Maryam Nowroozi, Samir Siksek

Let $E$ be an elliptic curve over the rationals given by an integral Weierstrass model and let $P$ be a rational point of infinite order. The multiple $n P$ has the form $(A_n/B_n^2…

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

New Algebraic Points on Curves

The modular approach to Diophantine equations over totally real fields

A single source theorem for primitive points on curves

Perfect powers in elliptic divisibility sequences

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