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papers [2019/08/09 01:08] admin |
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papers [2025/07/24 09:42] (current) admin [Published papers] |
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| ===== Published papers ===== |
- {{[[https:genfermat//doi.org/10.1016/j.jnt.2025.06.001 | Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve]], with Stefan Barańczuk and Matteo Verzobio, J. Number Theory (2026), Vol. 279, 170-export183. pdf(open access) |
- //[[https://rdcu.be/edbEv|The generalized Fermat equation Second moments and the bias conjecture for the family of cubic pencils]]//, with exponents Matija Kazalicki, Math. Z. 309, 72 (2025). 1-31. ([[https://arxiv.org/abs/2012.11306|preprint]]+[[https://bnaskrecki.faculty.wmi.amu.edu.pl/doku.php/second_moments|code]]) |
| - //[[https://doi.org/10.1007/s40828-024-00199-8|Periodic arrangements of closely packed spheres]]//, with Zbigniew Dauter and Mariusz Jaskolski, ChemTexts 11, 2 (2025). 1-17. (open access) |
| - //[[https://doi.org/10.1107/S2053273324010763|Growth functions of periodic space tessellations]]//, with Jakub Malinowski, Zbigniew Dauter and Mariusz Jaskolski, Acta Crystallogr., Sect. A: Found. Adv. (2025), Vol. 81, No. 1, 64-81. (open access) |
| - //[[https://doi.org/10.1017/prm.2024.7|Common valuations of division polynomials]]//, with Matteo Verzobio, Proc. A. R. Soc. Edinb. Published online (2024):1-15.(open access) |
- //[[https://aif.centre-mersenne.org/item/10.5802/aif.3635.pdf|Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6]]//, n}}with Julie Desjardins, Ann. Inst. Fourier 74 (2024) no.5 p. 2231-2274 (open access+[[https://zenodo.org/records/10659434|code]]) |
- //[[https://doi.org/10.1107/s160057672101205x | The Euler characteristic as a basis for teaching topology concepts to crystallographers]]//, with Nuno Freitas Zbigniew Dauter and Michael Stoll Mariusz Jaskólski, J. Appl. Cryst., (2022), Vol. 55, 154-167. (open access) |
- //[[https://arxivdoi.org/abs10.1016/1703j.05058jnt.2021.07.009|preprint versionDiophantine triples and K3 surfaces]]//, with Matija Kazalicki, J. Number Theory (2022), Compositio Mathematica Vol. 236, 41-70 (open access) |
| - //[[https://doi.org/10.1107/S2053273321004320 | A topological proof of the modified Euler characteristic based on the orbifold concept]]//, with Zbigniew Dauter and Mariusz Jaskólski, Acta Crystallogr., Sect. A: Found. Adv. (2021), Vol.7, No. 4, 317-326. (open access) |
| - //[[https://doi.org/10.1107/S2053273320016186 | Arithmetic proof of the multiplicity-weighted Euler characteristic for symmetrically arranged space-filling polyhedra]]//, with Zbigniew Dauter and Mariusz Jaskólski, Acta Crystallogr., Sect. A: Found. Adv. (2021), Vol.7, No. 2, 126-129. (open access) |
- //[[https://dx.doi.org/10.4310/CNTP.2020.v14.n4.a4|Arithmetic and geometry of a K3 surface emerging from virtual corrections to appearDrell-Yan scattering]]//, with Marco Besier, Dino Festi and Michael Harrison, Commun. Number Theory Phys. (2020), Vol. 14, No. 4, 863-911. (open access) |
| - //[[https://doi.org/10.1016/j.jnt.2019.12.002|Primitive divisors of elliptic divisiblity sequences over function fields with constant j-invariant]]//, with Marco Streng, J. Number Theory (2020), Vol. 213, 152-186. (open access) |
| - //[[https://doi.org/10.1112/S0010437X19007693|The generalized Fermat equation with exponents 2, 3, n]]//, with Nuno Freitas and Michael Stoll, Compos. Math., Vol. 156 (1) (2020), 77-113. (see also a [[http://www.setforbritain.org.uk/2017psr/M-NASKRECKI-3706-PSR.pdf| poster]] for [[http://www.setforbritain.org.uk/index.asp | STEM for Britain]]) ([[https://arxiv.org/abs/1703.05058|preprint version]]) |
- //[[https://wwwdoi.springer.comorg/gp10.1007/book/9783030125578 978-3-030-12558-5_7 |On higher congruences between cusp forms and Eisenstein series II]]//, Notes from the International Autumn School on Computational Number Theory: Izmir Institute of Technology 2017, Birkhäuser, 2019 ([[http://arxiv.org/abs/1810.02134|preprint version]]) |
- //[[http://nyjm.albany.edu/j/2016/22-46.html|Divisibility sequences of polynomials and heights estimates]]//, New York J. Math. 22 (2016), 989–-1020. (open access) |
- //[[httphttps://arxivdoi.org/abs/160910.04750|preprint version]]) |
4064/bc108-{{:bnaskrecki_distribution_of_mw_ranks.pdf0-16|Distribution of Mordell-Weil ranks of families of elliptic curves}}]]//, Banach Center Publications Publ. 108 (2016), 201-229,[[https://www.impan.pl/pl/wydawnictwa/banach(open access) |
- center-publications/all/108|DOI: 10.4064/bc108-0-16]] ([[httphttps://arxivdoi.org/abs/160910.04731|preprint version]]) |
- [[http://www.springer.com/mathematics/numbers/book1007/978-3-319-0384603847-96_10| On higher congruences between cusp forms and Eisenstein series]]// in Computations with Modular Forms © Springer-Verlag, Volume 6 , (2014), 257-277 . ([[http://arxiv.org/abs/1206.1881|preprint version]]) |
- //[[httphttps://journalswww.impan.pl/cgien/publishing-binhouse/doi?aa160journals-and-series/acta-arithmetica/all/160/2/83309/mordell-5 8211-weil-ranks-of-families-of-elliptic-curves-associated-to-pythagorean-triples |Mordell–Weil ranks of families of elliptic curves associated to Pythagorean triples]]//, Acta Arith. 160 (2013), 159-183([[http://arxiv. org/abs/1210.6933| preprint version]](open access) |
- //[[httphttps://pjmdoi.mathorg/10.berkeley.edu2140/involve/.2010/.3-3/p06.xhtml297|Infinite family of elliptic curves of rank at least 4]]//, Involve, Vol. 3(2010), No. 3 (2010), 297–316 ([[http://arxiv.org/abs/0909.3424| preprint version]]open access) |
| ===== Preprints ===== |
- Arithmetic and geometry //On the geography of a K3 surface emerging from virtual corrections to Drelllog--Yan scatteringsurfaces//, with Marco Besier, Dino Festi and Michael HarrisonPiotr Pokora, submitted ([[https://arxiv.org/abs/19082412.0107914635|preprint]] (+ [[drell_yan_k3s|code]]) |
- Primitive divisors //Explicit equations of elliptic divisiblity sequences over function fields with constant j800 conics on a Barth-invariant, with Marco StrengBauer quartic//, submitted([[https://arxiv.org/abs/19042108.1239313402 |preprint]]) |
| - //{{:hyper24111.pdf|On a certain hypergeometric motive of weight 2 and rank 3}}//, submitted ([[https://arxiv.org/abs/1702.07738|preprint]]) |
- //Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic forms//, submitted ([[http://arxiv.org/abs/1609.04715|preprint]]) |
===== In preparation ===== |
- Diophantine triples and K3 surfaces, with Matija Kazalicki, in preparation |
- Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6, with Julie Desjardins, in preparation |
- On realisations of weight 0 hypergeometric motives of small degrees, in preparation (with [[http://magma.maths.usyd.edu.au/magma/handbook/text/1516#17286|Magma package]]) |
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| ===== Popular writing ==== |
| * [[https://academia.pan.pl/czym-jest-szyfrowanie/|Czym jest szyfrowanie? (ACADEMIA (2023) No. 4 (76) pp. 18-21) ]] |
| * [[https://www.deltami.edu.pl/2024/05/jej-wysokosc-krzywa-eliptyczna/| Jej wysokość krzywa eliptyczna (Delta (2024) No. 5 (600) pp. 16-19)]] |
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| ===== In preparation ===== |
| - //Equiangular lines and an elliptic surface//, with Dan Fretwell and Neil I. Gillespie, in preparation |
| - //On realisations of weight 0 hypergeometric motives of small degrees//, in preparation (with [[http://magma.maths.usyd.edu.au/magma/handbook/text/1543#17716|Magma package]]) |
| ===== Theses ===== |
| //{{:bn_phd_thesis.pdf|"Rangi w rodzinach krzywych eliptycznych i formy modularne"}}//, Ph. D. thesis, 2014 |
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//{{:matma.pdf|"O pewnym równaniu diofantycznym"}}//, M. Sc. thesis, 2010 |
===== Online apps ===== |
- [[http://demonstrations.wolfram.com/NumericalIntegrationUsingRectanglesTheTrapezoidalRuleOrSimps|Numerical Integration using Rectangles, the Trapezoidal Rule, or Simpson's Rule from The Wolfram Demonstrations Project]] |
- [[http://demonstrations.wolfram.com/MotionOfASimplePendulumWithDamping|Motion of a Simple Pendulum with Damping from The Wolfram Demonstrations Project]] |
- [[http://demonstrations.wolfram.com/WorkInAnAttractiveInverseSquareField|Work in an Attractive Inverse-Square Field" from The Wolfram Demonstrations Project]] |
- [[http://demonstrations.wolfram.com/DrivenDampedOscillatorWithResonanceEffect|Driven Damped Oscillator with Resonance Effect" from The Wolfram Demonstrations Project]] |
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