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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.