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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
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papers
- Linear relations for coefficients of Drinfeld modular forms
Int. J. Number Theory, 4 (2008), 171-176
- Zeros of certain Drinfeld modular functions
J. Number Theory, 128 (2008), 1662-1669
- 2-adic and 3-adic part of class numbers and properties of central values of $L$-functions
Acta Arith., 147 (2011), 51-72
- 2-adic properties of modular functions associated to Fermat curves
Proc. Amer. Math. Soc., 139 (2011), 12; 4265-4271
- Congruent numbers and congruences between half-integral weight modular forms
J. Number Theory, 133 (2013), 4; 1079-1085
- Modular forms, hypergeometric functions and congruences
Ramanujan J., 34 (2014), 1-9
- Modular forms, de Rham cohomology and congruences (joint with A.J. Scholl)
Trans. Amer. Math. Soc. 368 (2016), 7097-7117
- Modular parametrizations of certain elliptic curves (joint with Y. Sakai and K. Tasaka)
Acta Arith., 163 (2014), 33-43
- 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.
- 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.
- 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
- On a special case of Watkins' conjecture (joint with D. Kohen)-correction
Proc. Amer. Math. Soc. 146 (2018), 541-545
- 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
- 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
- There are infinitely many rational Diophantine sextuples with square denominators (joint with A. Dujella and V. Petricevic)
J. Number Theory, 205 (2019), 340-346.
- 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.
- Rational D(q)-quadruples(joint with G. Drazic)
Indag. Math. (N.S.), Volume 33, Issue 2, March 2022, Pages 440-449
- 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
- Second moments and the bias conjecture for the family of cubic pencils (joint with B. Naskrecki)
preprint
- 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
- 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
- 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
- Quadratic twists of genus one curves and Diophantine quintuples
preprint
- Rational Diophantine sextuples with strong pair (joint with A. Dujella and V. Petricevic)
preprint
- Murmurations of Mestre-Nagao sums (joint with Z. Bujanovic and L. Novak)
IJDSMS Volume No. 02, Issue No. 01, pp. 51 - 61, (2024)
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