Asimina S. Hamakiotes

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20192026

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11 papers · 1 filter

math.NT2026

Average twin prime conjecture for elliptic curves in arithmetic progressions

Ahmet M. Güloğlu, Asimina S. Hamakiotes, Sung Min Lee +1

In 1988, Koblitz conjectured an asymptotic formula for the number of primes $p \leq x$ for which the reduction of an elliptic curve over $Q$ has prime order. Building on th…

math.NT2026

On the Density of Coprime Reductions of Elliptic Curves

Asimina S. Hamakiotes, Sung Min Lee, Jacob Mayle +1

Given non-CM elliptic curves $E_{1}$ and $E_{2}$ over $Q$ , we study the natural density of primes $p$ of good reduction for which the orders of the groups $E_{1} (F_{p})$ …

math.NT2025

Genus formulas for families of modular curves

Asimina S. Hamakiotes, Jun Bo Lau

For each open subgroup $H \leq GL_{2} (Z)$ , there is a modular curve $X_{H}$ , defined as a quotient of the full modular curve $X (N)$ , where $N$ is the l…

math.NT2024

Bounds for the relative class number problem for function fields

Santiago Arango-Piñeros, María Chara, Asimina S. Hamakiotes +2

We establish bounds on a finite separable extension of function fields in terms of the relative class number, thus reducing the problem of classifying extensions with a fixed relat…

math.NT2024

The maximal abelian extension contained in a division field of an elliptic curve over $Q$ with complex multiplication

Asimina S. Hamakiotes

Let $K$ be an imaginary quadratic field, and let $O_{K, f}$ be an order in $K$ of conductor $f \geq 1$ . Let $E$ be an elliptic curve with CM by $O_{K, f}$ , such th…

math.NT2024

Towards a classification of $p^{2}$ -discriminant ideal twins over number fields

Alyson Deines, Asimina S. Hamakiotes, Andreea Iorga +3

Isogenous elliptic curves have the same conductor but not necessarily the same minimal discriminant ideal. In this article, we explicitly classify all $p^{2}$ -isogenous elliptic curv…

math.NT2024

The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, II

John Cullinan, Shanna Dobson, Linda Frey +5

Let $E$ and $E^{'}$ be 2-isogenous elliptic curves over $\Q$. Following \cite{ck}, we call a good prime $p$ \emph{anomalous} if $E(\F_p) \simeq E'(\F_p)$ but $E(\F_{p^2}) \not \simeq…

math.NT2023

Elliptic curves with complex multiplication and abelian division fields

Asimina S. Hamakiotes, Alvaro Lozano-Robledo

Let $K$ be an imaginary quadratic field, and let $O_{K, f}$ be an order in $K$ of conductor $f \geq 1$ . Let $E$ be an elliptic curve with CM by $O_{K, f}$ , such th…

math.NT2023

Sums of Powers by L'Hopital's Rule

Eduardo Dueñez, Asimina S. Hamakiotes, Steven J. Miller

For a positive integer $d$ , let $p_{d} (n) := 0^{d} + 1^{d} + 2^{d} + \dots + n^{d}$ ; i.e., $p_{d} (n)$ is the sum of the first $d^{th}$ -powers up to $n$ . It's well known that $p_{d} (n)$ …

math.NT2019

Asymptotic Distribution of the Partition Crank

Asimina Hamakiotes, Aaron Kriegman, Wei-Lun Tsai

The partition crank is a statistic on partitions introduced by Freeman Dyson to explain Ramanujan's congruences. In this paper, we prove that the crank is asymptotically equidistri…

math.NT2019

Eta-quotients of Prime or Semiprime Level and Elliptic Curves

Michael Allen, Nicholas Anderson, Asimina Hamakiotes +2

From the Modularity Theorem proven by Wiles, Taylor, et al, we know that all elliptic curves are modular. It has been shown by Martin and Ono exactly which are represented by eta-q…

Average twin prime conjecture for elliptic curves in arithmetic progressions

On the Density of Coprime Reductions of Elliptic Curves

Genus formulas for families of modular curves

Bounds for the relative class number problem for function fields

The maximal abelian extension contained in a division field of an elliptic curve over Q with complex multiplication

Towards a classification of p2-discriminant ideal twins over number fields

The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, II

Elliptic curves with complex multiplication and abelian division fields

Sums of Powers by L'Hopital's Rule

Asymptotic Distribution of the Partition Crank

Eta-quotients of Prime or Semiprime Level and Elliptic Curves

The maximal abelian extension contained in a division field of an elliptic curve over $Q$ with complex multiplication

Towards a classification of $p^{2}$ -discriminant ideal twins over number fields