collaborators

6 papers

math.AG2026

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…

math.CO2026

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.

math.NT2026

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.

math.NT2025

The exceptional set in the abc conjecture

Christian Bernert

We study the size of the exceptional set in the conjecture, improving on and simplifying work of Browning, Lichtman and Teräväinen.

math.NT2025

Integral points of bounded height on quintic del Pezzo surfaces over number fields

Christian Bernert, Ulrich Derenthal

We prove an asymptotic formula for the number of integral points of bounded log-anticanonical height on split smooth quintic del Pezzo surfaces over number fields, with respect to…

math.NT2025

Points of bounded height on quintic del Pezzo surfaces over the rational numbers

Christian Bernert, Ulrich Derenthal

We give a relatively short and elementary proof of Manin's conjecture for split smooth quintic del Pezzo surfaces over the rational numbers.