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20172023
most citedA Positive Proportion of Hasse Principle Failures in a Family of Châtelet Surfaces

2 citations · 7 across the 8 of their papers we have counts for

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math.NT2022★ 2 cited

Weak approximation on the norm one torus

Peter Koymans, Nick Rome

For any abelian group , we prove an asymptotic formula for the number of -extensions of bounded discriminant such that the associated norm one torus $R_{K/\mat…

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…