Ekin Ozman

activity

20172026

collaborators

Showing math.NTShow all

7 papers · 1 filter

math.NT2026

Solving equations of signature $(p, p, 2)$ with coefficients over number fields

Begum Gulsah Cakti, Erman Isik, Yasemin Kara +1

Using the modular method, we study solutions to the Diophantine equation $A a^{p} + B b^{p} = C c^{2}$ over number fields. We first prove an asymptotic result for general number fields satisf…

math.NT2025

Non-trivial Solutions of $A a^{p} + B b^{p} = C c^{3}$ over Number Fields

Yasemin Kara, Stef Nomden, Ekin Özman

In this paper, we investigate solutions to the Diophantine equation $A a^{p} + B b^{p} = C c^{3}$ over number fields using the modular method. Assuming certain standard modularity conj…

math.NT2023

Iterated Monodromy Group of a PCF Quadratic Non-polynomial Map

Ozlem Ejder, Yasemin Kara, Ekin Ozman

We study the postcritically finite non-polynomial map $f (x) = \frac{1}{( x - 1 ) ^{2}}$ over a number field $k$ and prove various results about the geometric $G^{geom} (f)$ and arithm…

math.NT2023

Computing quadratic points on modular curves $X_{0} (N)$

Nikola Adžaga, Timo Keller, Philippe Michaud-Jacobs +3

In this paper we improve on existing methods to compute quadratic points on modular curves and apply them to successfully find all the quadratic points on all modular curves $X_0(N…

math.NT2019

Asymptotic Generalized Fermat's Last Theorem over Number Fields

Yasemin Kara, Ekin Ozman

Recent work of Freitas and Siksek showed that an asymptotic version of Fermat's Last Theorem holds for many totally real fields. Later this result was extended by Deconinck to gene…

math.NT2018

Quadratic Points on Modular Curves

Ekin Ozman, Samir Siksek

In this paper we determine the quadratic points on the modular curves X_0(N), where the curve is non-hyperelliptic, the genus is 3, 4 or 5, and the Mordell--Weil group of J_0(N) is…