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math.NT2025
Counting rational points on elliptic and hyperelliptic curves over function fields
Jean Gillibert, Emmanuel Hallouin, Aaron Levin
Combining -descent techniques with Riemann-Roch and Bézout's theorems, we give an upper bound on the number of rational points of bounded height on elliptic and hyperelliptic c…
math.NT2025
Arithmetic rank bounds for abelian varieties over function fields
Félix Baril Boudreau, Jean Gillibert, Aaron Levin
It follows from the Grothendieck-Ogg-Shafarevich formula that the rank of an abelian variety (with trivial trace) defined over the function field of a curve is bounded by a quantit…
math.NT2024
A New Diophantine Approximation Inequality on Surfaces and Its Applications
Keping Huang, Aaron Levin, Zheng Xiao
We prove a Diophantine approximation inequality for closed subschemes on surfaces which can be viewed as a joint generalization of recent inequalities of Ru-Vojta and Heier-Levin i…