Ekin Ozman

activity

20092026

most citedProvably weak instances of Ring-LWE

18 citations · 32 across the 17 of their papers we have counts for

collaborators

21 papers

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★ 7 cited

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.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

The Hasse Norm Principle in Global Function Fields

Adelina Mânzăţeanu, Rachel Newton, Ekin Ozman +2

Let $L$ be a finite extension of $F_{q} (t)$ . We calculate the proportion of polynomials of degree $d$ in $F_{q} [t]$ that are everywhere locally norms from $L/\mathbb{…

math.NT2019★ 2 cited

The boundary of the $p$ -rank $0$ stratum of the moduli space of cyclic covers of the projective line

Ekin Ozman, Rachel Pries, Colin Weir

We study the $p$ -rank stratification of the moduli space of cyclic degree $ℓ$ covers of the projective line in characteristic $p$ for distinct primes $p$ and $ℓ$ . The main re…

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…

math.NT2017

Non-ordinary curves with a Prym variety of low $p$ -rank

Turku Ozlum Celik, Yara Elias, Burcin Gunes +4

If $π : Y \to X$ is an unramified double cover of a smooth curve of genus $g$ , then the Prym variety $P_{π}$ is a principally polarized abelian variety of dimension $g - 1$ . When $X$ is…

math.NT2016

A bound on the primes of bad reduction for CM curves of genus 3

Pınar Kılıçer, Kristin Lauter, Elisa Lorenzo García +3

We give bounds on the primes of geometric bad reduction for curves of genus three of primitive CM type in terms of the CM orders. In the case of genus one, there are no primes of g…

math.NT2015

Ring-LWE Cryptography for the Number Theorist

Yara Elias, Kristin E. Lauter, Ekin Ozman +1

In this paper, we survey the status of attacks on the ring and polynomial learning with errors problems (RLWE and PLWE). Recent work on the security of these problems [Eisenträger-…

math.NT2015

The distribution of $F_{q}$ -points on cyclic $ℓ$ -covers of genus $g$

Alina Bucur, Chantal David, Brooke Feigon +4

We study fluctuations in the number of points of $ℓ$ -cyclic covers of the projective line over the finite field $F_{q}$ when $q \equiv 1 mod ℓ$ is fixed and the genus…

math.NT2015

Ordinary and almost ordinary Prym varieties

Ekin Ozman, Rachel Pries

We study the $p$ -rank stratification of the moduli space of Prym varieties in characteristic $p > 0$ . For arbitrary primes $p$ and $ℓ$ with $ℓ \neq = p$ and integers $g \geq…

cs.CR2015★ 18 cited

Provably weak instances of Ring-LWE

Yara Elias, Kristin E. Lauter, Ekin Ozman +1

The ring and polynomial learning with errors problems (Ring-LWE and Poly-LWE) have been proposed as hard problems to form the basis for cryptosystems, and various security reductio…

math.NT2014

Bad reduction of genus $3$ curves with complex multiplication

Irene Bouw, Jenny Cooley, Kristin Lauter +4

Let $C$ be a smooth, absolutely irreducible genus- $3$ curve over a number field $M$ . Suppose that the Jacobian of $C$ has complex multiplication by a sextic CM-field $K$ . Suppose f…

math.AG2013

Unramified Brauer classes on cyclic covers of the projective plane

Colin Ingalls, Andrew Obus, Ekin Ozman +1

Let X --> P^2 be a p-cyclic cover branched over a smooth, connected curve C of degree divisible by p, defined over a separably closed field of prime-to-p characteristic. We show th…

math.NT2012

Newton polygons for a variant of the Kloosterman family

Rebecca Bellovin, Sharon Anne Garthwaite, Ekin Ozman +3

We study the p-adic valuations of roots of L-functions associated with certain families of exponential sums of Laurent polynomials in n variables over a finite field. The families…

math.NT2012

On Polyquadratic Twists of X_0(N)

Ekin Ozman

In this paper, we study the local points of the twist of X_0(N) by a polyquadratic field and give an algorithm to produce such curves which has local points everywhere. Then we inv…

math.NT2009★ 3 cited

Local Points on Quadratic Twists of X_0(N)

Ekin Ozman

Let X^d(N) be the quadratic twist of the modular curve X_0(N) through the Atkin-Lehner involution w_N and a quadratic extension Q(\sqrt{d})/Q. The points of X^d(N)(Q) are precisely…

math.NT2009

Semi-direct Galois covers of the affine line

Linda Gruendken, Laura Hall-Seelig, Bo-Hae Im +3

Let $k$ be an algebraically closed field of characteristic $p > 0$ . Let $G$ be $Z / ℓ Z$ semi-direct product $Z / pZ$ where $ℓ$ is a prime distinct from $p$ . In this paper, we stud…

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

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

Iterated Monodromy Group of a PCF Quadratic Non-polynomial Map

Computing quadratic points on modular curves X0​(N)

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

The Hasse Norm Principle in Global Function Fields

The boundary of the p-rank 0 stratum of the moduli space of cyclic covers of the projective line

Asymptotic Generalized Fermat's Last Theorem over Number Fields

Quadratic Points on Modular Curves

Non-ordinary curves with a Prym variety of low p-rank

A bound on the primes of bad reduction for CM curves of genus 3

Ring-LWE Cryptography for the Number Theorist

The distribution of Fq​-points on cyclic ℓ-covers of genus g

Ordinary and almost ordinary Prym varieties

Provably weak instances of Ring-LWE

Bad reduction of genus 3 curves with complex multiplication

Unramified Brauer classes on cyclic covers of the projective plane

Newton polygons for a variant of the Kloosterman family

On Polyquadratic Twists of X_0(N)

Local Points on Quadratic Twists of X_0(N)

Semi-direct Galois covers of the affine line

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

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

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

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

The boundary of the $p$ -rank $0$ stratum of the moduli space of cyclic covers of the projective line

Non-ordinary curves with a Prym variety of low $p$ -rank

The distribution of $F_{q}$ -points on cyclic $ℓ$ -covers of genus $g$

Bad reduction of genus $3$ curves with complex multiplication