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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
Refinements on higher order Weil-Oesterlé bounds via a Serre type argument
Emmanuel Hallouin, Philippe Moustrou, Marc Perret
Weil's theorem gives the most standard bound on the number of points of a curve over a finite field. This bound was improved by Ihara and Oesterlé for larger genus. Recently, Hall…