Yasemin Kara

activity

20192026

most citedOn Ternary Diophantine Equations of Signature

(p, p, 3)

over Number Fields

2 citations · 3 across the 6 of their papers we have counts for

collaborators

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8 papers · 1 filter

math.NT2026

Arboreal Galois Groups of a PCF Map with Strictly Pre-periodic Critical Points

Özlem Ejder, Zofia Gołaska, Yasemin Kara +2

We study the arithmetic and geometric iterated monodromy groups associated to the postcritically finite (PCF) quadratic rational function $f (x) = \frac{2}{( x - 1 ) ^{2}}$ defined over a nu…

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.NT2024★ 1 cited

Non-trivial Integer Solutions of $x^{r} + y^{r} = D z^{p}$

Yasemin Kara, Diana Mocanu, Ekin Özman

In this paper, we use the modular method over totally real fields together with some standard conjectures (the Weak Frey--Mazur Conjecture and the Eichler--Shimura Conjecture) to p…

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.NT2022★ 2 cited

On Ternary Diophantine Equations of Signature $(p, p, 3)$ over Number Fields

Erman Isik, Yasemin Kara, Ekin Ozman

In this paper, we prove results about solutions of the Diophantine equation $x^{p} + y^{p} = z^{3}$ over various number fields using the modular method. Firstly, by assuming some standard mo…

math.NT2020

Construction of Poincaré-type series by generating kernels

Yasemin Kara, Moni Kumari, Jolanta Marzec +3

Let $Γ \subset PSL_{2} (R)$ be a Fuchsian group of the first kind having a fundamental domain with a finite hyperbolic area, and let $Γ$ be its cover in $\…

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…

Arboreal Galois Groups of a PCF Map with Strictly Pre-periodic Critical Points

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

Non-trivial Solutions of Aap+Bbp=Cc3 over Number Fields

Non-trivial Integer Solutions of xr+yr=Dzp