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math.NT2022★ 1 cited
The leading constant for rational points in families
Daniel Loughran, Nick Rome, Efthymios Sofos
We prove asymptotics for Serre's problem on the number of diagonal planar conics with a rational point and use this to put forward a new conjecture on counting the number of variet…
math.NT2022
Distribution of genus numbers of abelian number fields
Christopher Frei, Daniel Loughran, Rachel Newton
We study the quantitative behaviour of genus numbers of abelian extensions of number fields with given Galois group. We prove an asymptotic formula for the average value of the gen…