Matija Kazalicki
   [mkazal@math.hr] _



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research interests
~ connection between the arithmetic of Fourier coefficients of modular forms (for noncongruence subgroups) and algebraic geometry (Atkin and Swinnerton-Dyer congruences)
~ elliptic curves, modular forms and Galois representations
~ rational Diophantine m-tuples

abstracts of the papers
papers
  1. Linear relations for coefficients of Drinfeld modular forms
    Int. J. Number Theory, 4 (2008), 171-176
  2. Zeros of certain Drinfeld modular functions
    J. Number Theory, 128 (2008), 1662-1669
  3. 2-adic and 3-adic part of class numbers and properties of central values of $L$-functions
    Acta Arith., 147 (2011), 51-72
  4. 2-adic properties of modular functions associated to Fermat curves
    Proc. Amer. Math. Soc., 139 (2011), 12; 4265-4271
  5. Congruent numbers and congruences between half-integral weight modular forms
    J. Number Theory, 133 (2013), 4; 1079-1085
  6. Modular forms, hypergeometric functions and congruences
    Ramanujan J., 34 (2014), 1-9
  7. Modular forms, de Rham cohomology and congruences (joint with A.J. Scholl)
    Trans. Amer. Math. Soc. 368 (2016), 7097-7117
  8. Modular parametrizations of certain elliptic curves (joint with Y. Sakai and K. Tasaka)
    Acta Arith., 163 (2014), 33-43
  9. There are infinitely many rational Diophantine sextuples (joint with A. Dujella, M. Mikic and M. Szikszai )
    Int. Math. Res. Not. IMRN 2017 (2) (2017), 490-508.
  10. More on Diophantine sextuples (joint with A. Dujella)
    in Number Theory - Diophantine problems, uniform distribution and applications, Festschrift in honour of Robert F. Tichy's 60th birthday (C. Elsholtz, P. Grabner, Eds.), Springer-Verlag, Berlin, 2017, 227-235.
  11. Diophantine m-tuples in finite fields and modular forms (joint with A. Dujella)
    Res. number theory 7, 3 (2021). https://doi.org/10.1007/s40993-020-00232-y
  12. On a special case of Watkins' conjecture (joint with D. Kohen)-correction
    Proc. Amer. Math. Soc. 146 (2018), 541-545
  13. Supersingular zeros of divisor polynomials of elliptic curves of prime conductor (joint with D. Kohen)
    Res Math Sci (2017) 4: 10. https://doi.org/10.1186/s40687-017-0099-8
  14. Congruences for sporadic sequences and modular forms for non-congruence subgroups
    Res Math Sci (2019) 6: 28. https://doi.org/10.1007/s40687-019-0191-3
  15. There are infinitely many rational Diophantine sextuples with square denominators (joint with A. Dujella and V. Petricevic)
    J. Number Theory, 205 (2019), 340-346.
  16. Rational Diophantine sextuples containing two regular quadruples and one regular quintuple (joint with A. Dujella and V. Petricevic)
    Acta Mathematica Spalatensia 1 (2021), 19-27.
  17. Rational D(q)-quadruples(joint with G. Drazic)
    Indag. Math. (N.S.), Volume 33, Issue 2, March 2022, Pages 440-449
  18. D(n)-quintuples with square elements (joint with A. Dujella and V. Petricevic)
    Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 115 (2021), Article 172
  19. Second moments and the bias conjecture for the family of cubic pencils (joint with B. Naskrecki)
    preprint
  20. Diophantine triples and K3 surfaces (joint with B. Naskrecki,appendix by L. Lasic)
    J. Number Theory, 236 (2021), 41-70, https://doi.org/10.1016/j.jnt.2021.07.009
  21. Elliptic curves with torsion groups Z/8Z and Z/2Z × Z/6Z (joint with A. Dujella and J. C. Peral)
    Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 115 (2021), Article 169
  22. Ranks of elliptic curves and deep neural networks (joint with D. Vlah)
    Res. number theory 9, 53 (2023). https://doi.org/10.1007/s40993-023-00462-w
  23. Quadratic twists of genus one curves and Diophantine quintuples
    preprint
  24. Rational Diophantine sextuples with strong pair (joint with A. Dujella and V. Petricevic)
    preprint
  25. Murmurations of Mestre-Nagao sums (joint with Z. Bujanovic and L. Novak)
    preprint