Zobrazeno 1 - 10
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pro vyhledávání: '"Khawaja, Maleeha"'
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 hyperelliptic curves constructed by Kraus and Darmon in the study of th
Externí odkaz:
http://arxiv.org/abs/2410.21134
Autor:
Khawaja, Maleeha, Siksek, Samir
Wiles' proof of Fermat's last theorem initiated a powerful new approach towards the resolution of certain Diophantine equations over $\mathbb{Q}$. Numerous novel obstacles arise when extending this approach to the resolution of Diophantine equations
Externí odkaz:
http://arxiv.org/abs/2401.03099
Autor:
Khawaja, Maleeha, Siksek, Samir
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 $n \ge 2$. We say that an algebraic point $P \in C(\overline{K})$ has degree $n$ if the extension $K(P)/K$ has degree $n$. By t
Externí odkaz:
http://arxiv.org/abs/2401.03091
We study the equation $(x-4r)^3 + (x-3r)^3 + (x-2r)^3+(x-r)^3 + x^3 + (x+r)^3+(x+2r)^3 + (x+3r)^3 + (x+4r)^3 = y^p$, which is a natural continuation of previous works carried out by A. Arg\'{a}ez-Garc\'{i}a and the fourth author (perfect powers that
Externí odkaz:
http://arxiv.org/abs/2307.01815
Autor:
Khawaja, Maleeha, Siksek, Samir
A number field $K$ is primitive if $K$ and $\mathbb{Q}$ are the only subextensions of $K$. Let $C$ be a curve defined over $\mathbb{Q}$. We call an algebraic point $P\in C(\overline{\mathbb{Q}})$ primitive if the number field $\mathbb{Q}(P)$ is primi
Externí odkaz:
http://arxiv.org/abs/2306.17772
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 in recent years. In this survey, we present the key tools and techniqu
Externí odkaz:
http://arxiv.org/abs/2306.05168
Autor:
Khawaja, Maleeha
Publikováno v:
Research in Number Theory 10, 48 (2024)
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 $K$ such that $E$ has a $K$-rational point of order $p$. Derickx, Kamie
Externí odkaz:
http://arxiv.org/abs/2304.14284
Autor:
Khawaja, Maleeha, Jarvis, Frazer
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 equation over $\mathbb{Q}(\sqrt{2},\sqrt{3})$ for $n\geq 4$.
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Externí odkaz:
http://arxiv.org/abs/2210.03744
Publikováno v:
In Indagationes Mathematicae May 2024 35(3):500-515
Autor:
Khawaja, Maleeha, Siksek, Samir
Publikováno v:
Research in Number Theory; 6/4/2024, Vol. 10 Issue 3, p1-20, 20p