40 citations · 117 across the 23 of their papers we have counts for
24 papers · 1 filter
Gross vectors modulo 2 and elliptic curves of prime conductor
Matija Kazalicki, Siniša Slijepčević
Let p > 3 be a prime, and let S_p denote the geometric isomorphism classes of supersingular elliptic curves in characteristic p whose j-invariants lie in F_p. For each negative fun…
Quartic Rational Diophantine Quadruples and the Euler Surface
Alen Andrašek, Matija Kazalicki, Domagoj Vlah
We prove that there exist infinitely many quartic rational Diophantine quadruples, that is, sets of four pairwise distinct nonzero rational numbers whose pairwise products increase…
Seven squares from three numbers
Andrej Dujella, Matija Kazalicki, Vinko Petričević
We study triples {a,b,c} of distinct nonzero rational numbers such that a+1,b+1,c+1,ab+1,ac+1,bc+1 and abc+1 are all perfect squares. We prove that there exist infinitely many such…
Equidistribution of Diophantine pairs among the equivalence classes of quadratic forms
Goran Dražić, Matija Kazalicki, Rudi Mrazović
For a fixed integer n, a pair of nonzero integers {a, c} is called a D(n)-pair if the product ac plus n is a perfect square. In this short note we prove that D(n)-pairs are asympto…
Improving elliptic curve rank classification using multi-value and learned Mestre-Nagao sums
Zvonimir Bujanović, Matija Kazalicki, Domagoj Vlah
Determining the rank of an elliptic curve E/Q remains a central challenge in number theory. Heuristics such as Mestre--Nagao sums are widely used to estimate ranks, but there is co…
Murmurations of Mestre-Nagao sums
Zvonimir Bujanović, Matija Kazalicki, Lukas Novak
This paper investigates the detection of the rank of elliptic curves with ranks 0 and 1, employing a heuristic known as the Mestre-Nagao sum \[ S(B) = \frac{1}{\log{B}} \sum_{\subs…