Research
Research
Publications
(Links to Arxiv articles may differ from final published article)
Irreducible polynomials
(with I. E. Shparlinski) On the number of Eisenstein polynomials of bounded height <PDF>, Applied Algebra in Engineering, Communication and Computing 24, (2013), 149-156.
(with I. E. Shparlinski) On shifted Eisenstein polynomials <PDF>, Periodica Mathematica Hungarica 69, (2014), 170-181.
On the number of polynomials of bounded height that satisfy Dumas's criterion <PDF>, Journal of Integer Sequences 17, (2014).
(with I. E. Shparlinski) Counting irreducible binomials over finite fields <PDF>, Finite Fields and their Applications, 38, (2016), 1-12.
Pairwise coprimality
Pairwise non-primality of triples <PDF>, Preprint, 2013.
(with Juan Arias de Reyna) Counting tuples restricted by coprimality conditions <PDF>, Journal of Integer Sequences 10, (2015).
(with Juan Arias de Reyna) Tuples of polynomials over finite fields with pairwise coprimality conditions < PDF>, Finite Fields and their Applications, 53, (2018).
Floor function summations and sets
(with O. Bordellès, L. Dain, H. Pan, I. E. Shparlinski) On a sum involving the Euler function < PDF>, Journal of Number Theory, 202, (2019).
Cardinality of a floor function set <PDF>, Integers, 16, (2019), A67.
Primes in floor function sets <PDF>, Integers, 22, (2022), A59.
(with O. Bordellès, D. Nikolic) Sparse sets that satisfy the prime number theoreom <PDF>, Journal of Number Theory (to appear), 2023.
(with R. Miraj) On some floor function sets, Preprint, <PDF>
GCD and LCM Summations
A summation involving the divisor and GCD functions <PDF>, Journal of Integer Sequences 23, (2020).
(with L. Tóth) On certain sums of arithmetic functions involving the GCD and LCM of two positive integers <PDF>, Results in Mathematics (2021), 76:49.
A summation of the number of distinct prime divisors of the lcm <PDF>, Preprint 2021.
(with L. Tóth) Estimates for k-dimensional spherical summations of arithmetic functions for the GCD and LCM <PDF>, Number theory in memory of Eduard Wirsing, Springer Nature Switzerland AG, 2023.
(with L. Tóth) Hyperbolic summation for functions of the GCD and LCM of several integers < PDF>, The Ramanujan Journal (2022).
Other
(with I.E. Shparlinski) On the Greatest Common Divisor of shifted sets <PDF>, Journal of Number Theory 154, (2015), 63-73.
Evaluationally coprime linear polynomials <PDF>, Integers, 16, (2016), A65.
Conference Presentations
'Modular forms and the sums of four squares', Honours seminar, Sept 2011, University of New South Wales, Sydney.
'Modular forms and the sums of four squares', CARMA number theory seminar, Nov 2011, University of Newcastle, Newcastle.
'Counting polynomials that satisfy the Eisenstein criterion', 36th Australian Conference on Combinatorial Mathematics and Combinatorial Computing, Dec 2012, University of New South Wales, Sydney.
'Pairwise non-coprimality', Australian Mathematical Society, 57th Annual Conference, Oct 2013, University of Sydney, Sydney.
'The Eisenstein criterion and pairwise coprimality', Pure mathematics seminar, Sept 2014, University of New South Wales, Sydney.
'The approximate GCD problem', Number theory seminar, Apr 2015, University of New South Wales, Sydney.
'The approximate GCD problem', Australian Mathematical Society, 59th Annual Conference, Sept 2015, Flinders University, Adelaide.
'Pairwise coprimality', 5th Number Theory Down Under Conference, Oct 2017, Latrobe University, Bendigo.
Attended as Australian Mathematics Society delegate, Science meets Parliament 2018, Feb. 2018, Parliament House, Canberra.
'Pairwise coprimality', Integers conference, Oct 2018, Augusta, Georgia, United States of America.
'On a sum involving the Euler function', 7th Number Theory Down Under Conference, Oct 2019, University of New South Wales, Sydney.
'Sums of arithmetic functions involving the GCD and LCM', Australian Mathematical Society, 64th Annual Conference, Dec 2020, University of New England, held virtually.
'Primes in floor functions sets and sequences', Australian Mathematical Society, 65th Annual Conference, Dec 2021, University of Newcastle, held virtually.
'Floor function sets (and what has that got to do with the Prime Number Theory)', Oct 2022, Australian Defence Force Academy, Canberra.
'Primes in Floor Function Sets', Australian Mathematical Society, 66th Annual Conference, Dec 2022, University of New South Wales, Sydney.
`Primes in Floor Function Sets', Number Theory Down Under 11, Sep 2023, Australian National University