3 papers
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…
cs.IT2025
Ruled surfaces over finite fields, and some codes over them
Régis Blache, Emmanuel Hallouin
In the first part of this article, we consider ruled surfaces defined over a finite field; we introduce invariants for them, and describe some explicit contructions that illustrate…
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…