Mentzelos Melistas

activity

20212026

most citedA divisibility related to the Birch and Swinnerton-Dyer conjecture

1 citations · 1 across the 11 of their papers we have counts for

collaborators

14 papers

math.NT2026

Tamagawa numbers and torsion of elliptic curves over function fields

David Kurniadi Angdinata, Mentzelos Melistas

We study the divisibilities of Tamagawa numbers $c (E)$ of elliptic curves $E$ over global function fields $K$ in terms of their torsion subgroups $ E(K)_{\operatorname{tors}}…

math.NT2026

On a conjecture of Deines

Mentzelos Melistas

Two elliptic curves defined over $Q$ are called discriminant twins if they have the same minimal discriminant and the same conductor. Deines, in 2014, conjectured that the…

math.NT2025

Small Tamagawa numbers of elliptic curves with isogenies or torsion

Mentzelos Melistas

In this article with study Tamagawa numbers of elliptic curves defined over $Q$ that have isogenies or torsion points. More precisely, our aim is either to bound the set o…

math.NT2024

Low rank specializations of elliptic surfaces

Mentzelos Melistas

Let $E / Q (T)$ be a non-isotrivial elliptic curve of rank $r$ . A theorem due to Silverman implies that the rank $r_{t}$ of the specialization $E_{t} / Q$ is at least $r$ …

math.NT2024

Reduction types of CM curves

Mentzelos Melistas

We study the reduction properties of low genus curves whose Jacobian has complex multiplication. In the elliptic curve case, we classify the possible Kodaira types of reduction tha…

math.NT2023

Universal quadratic forms and Dedekind zeta functions

Vítězslav Kala, Mentzelos Melistas

We study universal quadratic forms over totally real number fields using Dedekind zeta functions. In particular, we prove an explicit upper bound for the rank of universal quadrati…

math.NT2023

Torsion and twists of abelian varieties

Mentzelos Melistas

In this article, we investigate the possible torsion subgroups of twists of abelian varieties with good reduction. As an application, we prove a theorem concerning ramified primes…

math.NT2023

Reduction and isogenies of elliptic curves

Mentzelos Melistas

Let $R$ be a complete discrete valuation ring with fraction field $K$ and perfect residue field $k$ of characteristic $p > 0$ . Let $E / K$ be an elliptic curve with a $K$ -rational isog…

math.NT2023

An analogue of a conjecture of Rasmussen and Tamagawa for abelian varieties over function fields

Mentzelos Melistas

Let $L$ be a number field and let $ℓ$ be a prime number. Rasmussen and Tamagawa conjectured, in a precise sense, that abelian varieties whose field of definition of the $ℓ$ -p…

math.NT2022★ 1 cited

A divisibility related to the Birch and Swinnerton-Dyer conjecture

Mentzelos Melistas

Let $E / Q$ be an optimal elliptic curve of analytic rank zero. It follows from the Birch and Swinnerton-Dyer conjecture for elliptic curves of analytic rank zero that the o…

math.NT2022

Tamagawa numbers of elliptic curves with torsion points

Mentzelos Melistas

Let $K$ be a global field and let $E / K$ be an elliptic curve with a $K$ -rational point of prime order $p$ . In this paper we are interested in how often the (global) Tamagawa number…

math.NT2021

Purely additive reduction of abelian varieties with torsion

Mentzelos Melistas

Let $O_{K}$ be a discrete valuation ring with fraction field $K$ of characteristic $0$ and algebraically closed residue field $k$ of characteristic $p > 0$ . Let $A / K$ be an…

math.NT2021

Integer Dynamics

Dino Lorenzini, Mentzelos Melistas, Arvind Suresh +2

Let $b \geq 2$ be an integer, and write the base $b$ expansion of any non-negative integer $n$ as $n = x_{0} + x_{1} b + \dots + x_{d} b^{d}$ , with $x_{d} > 0$ and $0 \leq x_{i} < b$ for $i=0,\dots,…

math.NT2021

On a conjecture of Agashe

Mentzelos Melistas

Let $E / Q$ be an optimal elliptic curve, $- D$ be a negative fundamental discriminant coprime to the conductor $N$ of $E / Q$ and let $E^{- D} / Q$ be the twist…