B. Naskrȩcki

activity

20092026

most citedMordell-Weil ranks of families of elliptic curves associated to Pythagorean triples

9 citations · 37 across the 17 of their papers we have counts for

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12 papers · 1 filter

math.NT2022★ 2 cited

Common valuations of division polynomials

Bartosz Naskręcki, Matteo Verzobio

In this note we prove a formula for the cancellation exponent $k_{v, n}$ between division polynomials $ψ_{n}$ and $ϕ_{n}$ associated with a sequence ${n P}_{n \in N}$ of points…

math.NT2021

Diophantine triples and K3 surfaces

Matija Kazalicki, Bartosz Naskręcki

A Diophantine $m$ -tuple with elements in the field $K$ is a set of $m$ non-zero (distinct) elements of $K$ with the property that the product of any two distinct elements is one le…

math.NT2019★ 3 cited

Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6

Julie Desjardins, Bartosz Naskręcki

In this paper, we give an effective and efficient algorithm which on input takes non-zero integers $A$ and $B$ and on output produces the generators of the Mordell-Weil group of th…

math.NT2019

Primitive divisors of elliptic divisibility sequences over function fields with constant j-invariant

Bartosz Naskręcki, Marco Streng

We prove an optimal Zsigmondy bound for elliptic divisibility sequences over function fields in case the $j$ -invariant of the elliptic curve is constant. In more detail, given an e…

math.NT2017★ 2 cited

The generalized Fermat equation with exponents 2, 3, n

Nuno Freitas, Bartosz Naskrecki, Michael Stoll

We study the Generalized Fermat Equation $x^{2} + y^{3} = z^{p}$ , to be solved in coprime integers, where $p \geq 7$ is prime. Using modularity and level lowering techniques, the problem…

math.NT2017★ 7 cited

On a certain hypergeometric motive of weight 2 and rank 3

Bartosz Naskrecki

We study a family of hypergeometric motives $H (α, β ∣ t)$ attached to a pair of tuples $α = (1/4, 1/2, 3/4)$ , $β = (0, 0, 0)$ . To each such motive we can attach a system of $ℓ$ --adic reali…

math.NT2016★ 3 cited

Divisibility sequences of polynomials and heights estimates

Bartosz Naskręcki

In this note we compute a constant $N$ that bounds the number of non--primitive divisors in elliptic divisibility sequences over function fields of any characteristic. We improve a…

math.NT2016★ 3 cited

Distribution of Mordell--Weil ranks of families of elliptic curves

Bartosz Naskręcki

We discuss the distribution of Mordell--Weil ranks of the family of elliptic curves $y^{2} = (x + α f^{2}) (x + β b g^{2}) (x + γ h^{2})$ where $f, g, h$ are coprime polynomials that parametrize the proj…

math.NT2016★ 1 cited

Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic forms

Bartosz Naskręcki

We prove results on the Mordell--Weil rank of elliptic curves $y^{2} = x (x - α a^{2}) (x - β b^{2})$ parametrized by binary quadratic forms $α a^{2} + β b^{2} = γ c^{2}$ . We express our explicit lower bounds…

math.NT2012★ 9 cited

Mordell-Weil ranks of families of elliptic curves associated to Pythagorean triples

Bartosz Naskręcki

We study the family of elliptic curves $y^{2} = x (x - a^{2}) (x - b^{2})$ parametrized by Pythagorean triples $(a, b, c)$ . We prove that for a generic triple the lower bound of the rank of the Mo…

math.NT2012★ 4 cited

On higher congruences between cusp forms and Eisenstein series

Bartosz Naskręcki

In this paper we present several finite families of congruences between cusp forms and Eisenstein series of higher weights at powers of prime ideals. We formulate a conjecture whic…

math.NT2009

Infinite family of elliptic curves of rank at least 4

Bartosz Naskrecki

We investigate $Q$ -ranks of the elliptic curve $E_{t}$ : $y^{2} + t x y = x^{3} + t x^{2} - x + 1$ where $t$ is a rational parameter. We prove that for infinitely many values of $t$ the rank of…