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math.NT2025
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…
math.NT2024
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…