Matija Kazalicki
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student projects
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
  1. Linear relations for coefficients of Drinfeld modular forms
    International Journal of Number Theory, 4 (2008), pp. 171-176
  2. Zeros of certain Drinfeld modular functions
    Journal of Number Theory, 128 (2008), pp. 1662-1669
  3. 2-adic and 3-adic part of class numbers and properties of central values of $L$-functions
    Acta Arithmetica, 147 (2011), pp. 51-72
  4. 2-adic properties of modular functions associated to Fermat curves
    Proceedings of AMS, 139 (2011), 12; pp. 4265-4271
  5. Congruent numbers and congruences between half-integral weight modular forms
    Journal of number theory, 133 (2013), 4;pp. 1079-1085
  6. Modular forms, hypergeometric functions and congruences
    The Ramanujan Journal, 34 (2014), pp. 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 Arithmetica, 163 (2014), pp. 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, pp. 227-235.
  11. Diophantine m-tuples in finite fields and modular forms (joint with A. Dujella)
  12. On a special case of Watkins' conjecture (joint with D. Kohen)
    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.