Christian Bernert

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20232026

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math.NT2024

Bounds on the exceptional set in the $ab c$ conjecture

Christian Bernert, Tim Browning, Jared Duker Lichtman +1

We study solutions to the equation $a + b = c$ , where $a, b, c$ form a triple of coprime natural numbers. The $ab c$ conjecture asserts that, for any $ε > 0$ , such triples satisfy $\mathrm{…

math.NT2024

Points of bounded height on quintic del Pezzo surfaces over number fields

Christian Bernert, Ulrich Derenthal

We prove Manin's conjecture for split smooth quintic del Pezzo surfaces over arbitrary number fields with respect to fairly general anticanonical height functions. After passing to…

Bounds on the exceptional set in the abc conjecture

Points of bounded height on quintic del Pezzo surfaces over number fields

Bounds on the exceptional set in the $ab c$ conjecture