5 papers · 1 filter
Equidistribution and the torsor method
Christian Bernert, Ulrich Derenthal, Florian Wilsch
We prove equidistribution and Manin's conjecture for rational points outside the lines on smooth split quintic del Pezzo surfaces over number fields with respect to any anticanonic…
Motivic counting of curves on split quintic del Pezzo surfaces
Christian Bernert, Loïs Faisant, Jakob Glas
We prove the "all-the-heights'' version of the Batyrev--Manin--Peyre conjecture for split quintic del Pezzo surfaces, both for counting rational points over global function fields…
The inverse problem for the Steiner--Wiener index via additive number theory
Christian Bernert, Joshua Shaw
We show that, for any given , every sufficiently large number appears as the Steiner--Wiener index of a graph.
Side lengths of cubes with vertices in
Christian Bernert, Jens Reinhold
We determine the set of side lengths of -dimensional cubes with vertices in using Witt's cancellation theorem from the algebraic theory of quadratic forms.
Integral points over number fields: a Clemens complex jigsaw puzzle
Christian Bernert, Ulrich Derenthal, Judith Ortmann +1
We prove an asymptotic formula for the number of integral points of bounded log anticanonical height on a singular quartic del Pezzo surface over arbitrary number fields, with resp…