dr hab. Andrzej Dąbrowski, prof. US

    dr hab. Andrzej Dąbrowski, prof. US

    • Informacje ogólne

      Stopień naukowy: doktor habilitowany
      Stanowisko: profesor
      Zakład: Zakład Teorii Liczb
      Numer pokoju: 22, 23/ 20
      Telefon: +48 91 444 12 61+48 91 444 12 64
      E-mail: andrzej.dabrowski@usz.edu.pl
      Konsultacje: czwartek 13:00 – 14:30
    • Obszar działalności naukowej:

      Arytmetyczna Geometria Algebraiczna, Teoria Liczb, Teoria Iwasawy, Formy modularne i reprezentacje Galois, Teoria kryptografii.

    • Publikacje

      1. A. Dąbrowski, Admissible p-adic L-functions of automorphic forms, Vestnik MGU (Ser. Mat.) 2 (1993), 8-12 (in Russian); English transl.: Moscow Univ. Math. Bull. 48 (1993), 6-10.
      2. A. Dąbrowski, Admissible motives, p-adic L-functions and symmetric squares of modular forms. In: Selected topics in Algebra, Geometry and Discrete Mathematics (ed. A. I. Kostrikin, O. B. Lupanov), Moscow State Univ. Press (1992), 26-47 (in Russian).
      3. A. Dąbrowski, p-adic L-functions of Hilbert modular forms, Ann. Inst. Fourier 44 (1994), 1025-1041.
      4. A. Dąbrowski, On integral representations and critical values of certain tensor product L-functions, Max Planck Institut fur Math. preprint 56, Bonn (1994).
      5. A. Dąbrowski, Mixed motives over Z and p-adic L-functions, Max Planck Institut fur Math. preprint 100, Bonn (1994).
      6. A. Dąbrowski, On Poincare series on Spm, Math. Zeitschrift 221 (1996), 573-589.
      7. A. Dąbrowski, A note on values of the Riemann zeta function at positive odd integers, Nieuw Archief voor Wiskunde 14 (1996), 199-207. Pobierz plik (zetavalues.pdf)
      8. A. Dąbrowski, On the diophantine equation x!+A = y^2, Nieuw Archief voor Wiskunde 14 (1996), 321-324. Pobierz plik (brocardramanujan.pdf)
      9. A. Dąbrowski, On the symmetric power of an elliptic curve, Contemporary Math. 199 (1996), 59-82.
      10. A. Dąbrowski, D. Delbourgo, S-adic L-functions attached to the symmetric square of a newform, Proc. London Math. Soc. 74 (1997), 559-611.
      11. A. Dąbrowski, On p-adic q-ζ-functions, Journal of Number Theory 64 (1997), 100-103.
      12. A. Dąbrowski, Simple proof of some combinatorial result in the theory of automorphic pseudodierential operators, Journal of Combin. Theory (series A) 80 (1997), 385-387.
      13. A. Dąbrowski, On certain L-series of Rankin-Selberg type associated to Siegel modular forms of degree 2, Archiv der Math. 70 (1998), 297-306.
      14. A. Dąbrowski, M. Wieczorek, Arithmetic on certain families of elliptic curves, Bulletin of the Australian Math. Society 61 (2000), 319-327.
      15. A. Dąbrowski, On zeta functions associated with polynomials, Bulletin of the Australian Math. Society 61 (2000), 455-458.
      16. A. Dąbrowski, M. Wieczorek, Families of elliptic curves with trivial Mordell-Weil group, Bulletin of the Australian Math. Society 62 (2000), 303-306.
      17. A. Dąbrowski, J. Pomykała, Nonvanishing of motivic L-functions, Mathematical Proceedings of the Cambridge Philosophical Society 130 (2001), 221-235.
      18. A. Dąbrowski, On admissible distributions attached to convolutions of Hilbert modular forms, Bulletin of the Australian Math. Society 64 (2001), 63-70.
      19. A. Dąbrowski, J. Pomykała, On zeros of motivic L-functions, Mathematical Proceedings of the Cambridge Philosophical Society 134 (2003), 421-432.
      20. A. Dąbrowski, M. Wieczorek, On the equation y^2 = x(x-2^m)(x+q -2^m), Journal of Number Theory 124 (2007), 364-379.
      21. A. Dąbrowski, On the integers represented by x^4-y^4, Bull. AustralianMath. Soc. 76 (2007), 133-136.
      22. A. Dąbrowski, Modularity of elliptic curves and Fermat’s Last Theorem, Wiadomosci Matematyczne 43 (2007), 3-47; errata in 44 (2008), 137 (in Polish).
      23. A. Dąbrowski, On the proportion of rank 0 twists of elliptic curves, Comptes Rendus Acad. Sci. Paris, Math. 346 (2008), 483-486.
      24. A. Dąbrowski, M. Wodzicki, Elliptic curves with large analytic order of the Tate-Shafarevich group, Algebra, Arithmetic and Geometry – In honor of Y.I. Manin, Progress in Math. 269 (2009), 407-421.
      25. A. Dąbrowski, Serre’s modularity conjecture and new proofs of Fermat’s last theorem, Wiadomosci Matematyczne 45 (2009), 3-24 (in Polish).
      26. A. Dąbrowski, T. Jędrzejak, Ranks in families of Jacobian varieties of twisted Fermat curves, Canad. Math. Bull. 53 (2010), 58-63.
      27. A. Dąbrowski, On a class of generalized Fermat equations, Bull. Aust. Math. Soc. 82 (2010), 505-510.
      28. A. Dąbrowski, Bounded p-adic L-functions of motives at supersingular primes, Comptes Rendus Acad. Sci. Paris, Math. 349 (2011), 365-368.
      29. A. Dąbrowski, On the Lebesgue-Nagell equation, Colloquium Math. 125 (2) (2011), 245-253.
      30. A. Dąbrowski, On the Brocard-Ramanujan problem and generalizations, Colloquium Math. 126 (1) (2012), 105-110.
      31. A. Dąbrowski, T. Jędrzejak, K. Krawciów, Cubic forms, powers of primes and the Kraus method, Colloquium Math. 128(1) (2012), 35-48.
      32. A. Dąbrowski, M. Ulas, Variations on the Brocard-Ramanujan equation, Journal of Number Theory 133 (2013), 1168-1185.
      33. A. Dąbrowski, A note on p-adic q-ζ-functions II, Journal of Mathematical Analysis and Applications 411 (2014), 873-875.
      34. A. Dąbrowski, A family of pairing-friendly superelliptic curves of genus 4, Cryptology and Cybersecurity, National Security Studies IV(6) (2014), 133-137.
      35. A. Dąbrowski, Average rank of elliptic curves in the works of Manjul Bhargava, WiadomosciMatematyczne 51(2) (2015), 219-237 (in Polish)
      36. A. Dąbrowski, T. Jędrzejak, L. Szymaszkiewicz, Behaviour of the order of Tate-Shafarevich groups for the quadratic twists of X0(49). In: Elliptic Curves, Modular Forms and Iwasawa Theory (In honour of John H. Coates’ 70th birthday), Springer Proceedings in Mathematics and
        Statistics 188 (2016), 125-159.
      37. A. Dąbrowski, L. Szymaszkiewicz, Orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves, Mathematics of Computation 87 (2018)
      38. A. Dąbrowski, L. Szymaszkiewicz, Behaviour of the order of Tate-Shafarevich groups for the quadratic twists of elliptic curves, arXiv: 1611.07840[math.NT]
    • Seminaria

      Geometria Diofantyczna (A. Dąbrowski), wtorek 12.00 – 15.00, s. 205A;
      Tematyka: arytmetyka rozmaitosci algebraicznych, L-funkcje form automorficznych, teoria Iwasawy. Seminarium jest czesciowo szkoleniowe (analityczne metody w geometrii diofantycznej, p-adyczne L-funkcje), ale sa tez omawiane wyniki wlasne oraz nowe wyniki z Arytmetycznej Geometrii Algebraicznej (dowod hipotezy Serre’a, zastosowanie krzywych eliptycznych i form modularnych do rownan typu Fermata, itp.).
      Seminarium istnieje od roku akademickiego 1998/1999.

    • Konferencje

      • LECTURES ON IWASAWA THEORY OF ELLIPTIC CURVES by John Coates (Cambridge), 21-23 marca 2017, organizator: A. Dąbrowski, Plan wykładów Pobierz plik (Coates marzec 2017.pdf)
      • Konferencja Kryptografia i bezpieczeństwo informacji, Warszawa, 5-6 czerwca 2014, A. Dąbrowski członek komitetu naukowego,
      • „Classical and modular approaches to exponential Diophantine equations”, Max-Planck-Institut fuer Mathematik, Bonn, 13-14 lutego 2007, organizatorzy: Andrzej Dąbrowski i Pieter Moree.
      • ASPEKTY GEOMETRII NIEPRZEMIENNEJ, Szczecin, 5-15 czerwca 2002, organizator: A. Dąbrowski.