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)
    Math. Z. 309, 72 (2025). https://doi.org/10.1007/s00209-025-03701-1
  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
    Res. number theory 11, 72 (2025). https://doi.org/10.1007/s40993-025-00652-8
  24. Rational Diophantine sextuples with strong pair (joint with A. Dujella and V. Petricevic)
    Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 119, 36 (2025)
  25. Murmurations of Mestre-Nagao sums (joint with Z. Bujanovic and L. Novak)
    IJDSMS Volume No. 02, Issue No. 01, pp. 51 - 61, (2024)
  26. Improving elliptic curve rank classification using multi-value and learned Mestre-Nagao sums (joint with Z. Bujanovic and D. Vlah)
    to appear in IJDSMS