Eleni Agathocleous

• PhD Mathematics University of Maryland College Park USA
• Postdoctoral Fellow at Deutsches Elektronen-Synchrotron

We study an infinite family of $j$-invariant zero elliptic curves $E_{D}:y^{2}=x^{3}+16D$ and their $\lambda$-isogenous curves $E_{D'}:y^{2}=x^{3}-27\cdot16D$, where $D$ and $D' = -3D$ are fundamental discriminants of a specific form, and $\lambda$ is an isogeny of degree $3$. A result of Honda guarantees that for our discriminants $D$, the quadrat...

We call a pair of distinct prime powers $(q_1,q_2) = (p_1^{a_1},p_2^{a_2})$ a Hasse pair if $|\sqrt{q_1}-\sqrt{q_2}| \leq 1$. For such pairs, we study the relation between the set $\mathcal{E}_1$ of isomorphism classes of elliptic curves defined over $\mathbb{F}_{q_1}$ with $q_2$ points, and the set $\mathcal{E}_2$ of isomorphism classes of ellipti...

Leonardi and Ruiz-Lopez recently proposed an additively homomorphic public key encryption scheme based on combining group homomorphisms with noise. Choosing parameters for their primitive requires choosing three groups G, H, and K. In their paper, Leonardi and Ruiz-Lopez claim that when G, H, and K are abelian, then their public key cryptosystem is...

In [15], Leonardi and Ruiz-Lopez propose an additively homomorphic public-key encryption scheme whose security is expected to depend on the hardness of the learning homomorphism with noise problem (LHN). Choosing parameters for their primitive requires choosing three groups G, H, and K. In their paper, Leonardi and Ruiz-Lopez claim that, when G, H,...

In [15], Leonardi and Ruiz-Lopez propose an additively homomorphic public key encryption scheme whose security is expected to depend on the hardness of the learning homomorphism with noise problem (LHN). Choosing parameters for their primitive requires choosing three groups $G$, $H$, and $K$. In their paper, Leonardi and Ruiz-Lopez claim that, when...

We study the family of elliptic curves $E_{D'}: y^{2} = x^{3} + 16D'$, where $D < -4$ is a negative squarefree integer that satisfies two simple congruence conditions. By assuming finiteness of their Tate-Shafarevich group, we show that these curves must have odd rank. We then focus on the subfamily of those elliptic curves $E_{D'}$ that correspond...

In this paper we study the structure of the $3-$part of the ideal class group of a certain family of real cyclotomic fields with $3-$class number exactly $9$ and conductor equal to the product of two distinct odd primes. We employ known results from Class Field Theory as well as theoretical and numerical results on real cyclic sextic fields, and we...

The class numbers $h^{+}$ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows and methods employing Leopoldt's decomposition of the class number become hard to use when the field extension is not cyclic of prime power. This is why other methods have been dev...

The class numbers h + of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows, and methods employing Leopoldt’s decomposition of the class number become hard to use when the field extension is not cyclic of prime power. This is why other methods have been develo...

The class numbers h+ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows and that is why other methods have been developed, which approach the problem from different angles. In this thesis we extend a method of Schoof that was designed for real cyclotomic fi...

There has been a rapid increase in the volume of research papers focusing on mathematics teacher education and in particular on the characteristics that should describe the desired mathematical knowledge for teachers. In this paper, it is suggested through theoretical discussion on the character of Abstract Algebra and via Peirce's semiotics, that...