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

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, to appear.
  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)
    Proceedings of AMS, to appear
  13. Supersingular zeros of divisor polynomials of elliptic curves of prime conductor (joint with D. Kohen)
    Res Math Sci (2017) 4: 10.