S. Siksek

activity

20042026

most citedThe Asymptotic Fermat's Last Theorem for Five-Sixths of Real Quadratic Fields

41 citations · 198 across the 39 of their papers we have counts for

collaborators

46 papers

math.NT2026

Hilbert's Irreducibility for $G_{m}$

Michael Stoll, Samir Siksek

Let $K$ be a number field and $S$ a finite set of non-archimedean places. Write $O_{S}$ for the ring of $S$ -integers of $K$ and $O_{S}^{\times}$ for its unit group. L…

math.NT2026

On a character-twisted analogue of Schäffer's equation

Kálmán Györy, Vandita Patel, Ákos Pintér +1

Let $f$ be a positive integer, and let $χ$ be a primitive quadratic character of conductor $f$ . Let $k$ be a positive integer, and write $B_{k} (χ, X)$ for the $k$ -th Bernoulli polynom…

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

Curves with few bad primes over cyclotomic $Z_{ℓ}$ -extensions

Samir Siksek, Robin Visser

Let $K$ be a number field, and $S$ a finite set of non-archimedean places of $K$ , and write $O_{S}^{\times}$ for the group of $S$ -units of $K$ . A famous theorem of Siegel ass…

math.NT2022★ 1 cited

Efficient resolution of Thue-Mahler equations

Adela Gherga, Samir Siksek

A Thue-Mahler equation is a Diophantine equation of the form $F (X, Y) = a \cdot p_{1}^{z_{1}} \dots p_{v}^{z_{v}}, g cd (X, Y) = 1$ where $F$ be an irreducible homogeneous binary form o…

math.NT2021★ 8 cited

Differences between perfect powers : prime power gaps

Michael A. Bennett, S. Siksek

We develop machinery to explicitly determine, in many instances, when the difference $x^{2} - y^{n}$ is divisible only by powers of a given fixed prime. This combines a wide variety of t…