1 citations · 2 across the 12 of their papers we have counts for
15 papers
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 cu…
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…
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, Hallo…
Integral points on elliptic curves with -invariant over
Jean Gillibert, Emmanuel Hallouin, Aaron Levin
We consider elliptic curves defined by an equation of the form , where has coefficients in a perfect field of characteristic not or . By perfor…
Classification of singular del Pezzo surfaces over finite fields
Régis Blache, Emmanuel Hallouin
In this article, we consider weak del Pezzo surfaces defined over a finite field, and their associated, singular, anticanonical models. We first define arithmetic types for such su…
Construction of good codes from weak Del Pezzo surfaces
Régis Blache, Emmanuel Hallouin
We construct algebraic geometric codes from weak del Pezzo surfaces. The codes are associated to the anti-canonical class of the anti-canonical model and to the set of rational poi…