L. Szymaszkiewicz

activity

20142021

most citedBehaviour of the order of Tate-Shafarevich groups for the quadratic twists of elliptic curves

4 citations · 4 across the 5 of their papers we have counts for

collaborators

8 papers

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.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…

math.NT2018

Orders of Tate-Shafarevich groups for the cubic twists of $X_{0} (27)$

Andrzej Dąbrowski, Lucjan Szymaszkiewicz

This paper continues the authors previous investigations concerning orders of Tate-Shafarevich groups in quadratic twists of a given elliptic curve, and for the family of the Neuma…

math.NT2016

Orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves

Andrzej Dąbrowski, Lucjan Szymaszkiewicz

We present the results of our search for the orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves.

math.NT2016★ 4 cited

Behaviour of the order of Tate-Shafarevich groups for the quadratic twists of elliptic curves

Andrzej Dąbrowski, Lucjan Szymaszkiewicz

We present the results of our search for the orders of Tate-Shafarevich groups for the quadratic twists of elliptic curves. We formulate a general conjecture, giving for a fixed el…

math.CO2015

Arcs in $Z_{2 p}^{2}$

Zofia Stępień, Lucjan Szymaszkiewicz

An arc in $Z_{n}^{2}$ is defined to be a set of points no three of which are collinear. We describe some properties of arcs and determine the maximum size of arcs for some small $n$ .

math.CO2014

A note on the no-three-in-line problem on a torus

Zofia Stȩpień, Aleksander Misiak, Alicja Szymaszkiewicz +2

In this paper we show that at most $2 g cd (m, n)$ points can be placed with no three in a line on an $m \times n$ discrete torus. In the situation when $g cd (m, n)$ is a prime, we com…

Critical L-values of Gross curves

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

Critical L-values for some quadratic twists of Gross curves

Orders of Tate-Shafarevich groups for the cubic twists of X0​(27)

Orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves

Behaviour of the order of Tate-Shafarevich groups for the quadratic twists of elliptic curves

Arcs in Z2p2​

A note on the no-three-in-line problem on a torus

Critical $L$ -values of Gross curves

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

Orders of Tate-Shafarevich groups for the cubic twists of $X_{0} (27)$

Arcs in $Z_{2 p}^{2}$