11 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…
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…
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.
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…
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.