A. Dkabrowski

activity

20192021

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math.NT2021

Critical $L$ -values of Gross curves

Andrzej Dąbrowski, Tomasz Jędrzejak, Lucjan Szymaszkiewicz

Let $K = Q (- q)$ , where $q$ is a prime congruent to $3$ modulo $4$ . Let $A = A (q)$ denote the Gross curve over the Hilbert class field $H$ of $K$ . In this note we use…

math.NT2021

Elliptic curves with exceptionally large analytic order of the Tate-Shafarevich groups

Andrzej Dąbrowski, Lucjan Szymaszkiewicz

We exhibit $88$ examples of rank zero elliptic curves over the rationals with $|\sza(E)| > 63408^2$, which was the largest previously known value for any explicit curve. Our record…

math.NT2020

On a class of Lebesgue-Ljunggren-Nagell type equations

Andrzej Dąbrowski, Nursena Günhan, Gökhan Soydan

Given odd, coprime integers $a$ , $b$ ( $a > 0$ ), we consider the Diophantine equation $a x^{2} + b^{2 l} = 4 y^{n}$ , $x, y \in Z$ , $l \in N$ , $n$ odd prime, $g cd (x, y) = 1$ . We completely…

math.NT2019

Critical $L$ -values for some quadratic twists of Gross curves

Andrzej Dąbrowski, Tomasz Jędrzejak, Lucjan Szymaszkiewicz

Let $K = Q (- q)$ , where $q$ is a prime congruent to $3$ modulo $4$ . Let $A = A (q)$ denote the Gross curve. Let $E = A^{(- β)}$ denote its quadratic twist, with $β = - q$ . T…

Critical L-values of Gross curves

Elliptic curves with exceptionally large analytic order of the Tate-Shafarevich groups

On a class of Lebesgue-Ljunggren-Nagell type equations

Critical L-values for some quadratic twists of Gross curves

Critical $L$ -values of Gross curves

Critical $L$ -values for some quadratic twists of Gross curves