Yasemin Kara

collaborators

4 papers

math.NT2026

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

Ãzlem Ejder, Zofia GoÅaska, 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

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

Yasemin Kara, Stef Nomden, Ekin Ãzman

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.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 Integer Solutions of $x^{r} + y^{r} = D z^{p}$

Yasemin Kara, Diana Mocanu, Ekin Ãzman +1

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…

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

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

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

Non-trivial Integer Solutions of xr+yr=Dzp

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

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

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