Diophantine stability and second order terms

Carlo Pagano; Efthymios Sofos

Diophantine stability and second order terms

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arxiv 2409.12144 v1 pith:MFDEIJSD submitted 2024-09-18 math.NT

Carlo Pagano , Efthymios Sofos This is my paper · ORCID

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keywords diophantineordersecondstabilityassociatedasymptoticbiascurve

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abstract

We establish a Galois-theoretic trichotomy governing Diophantine stability for genus $0$ curves. We use it to prove that the curve associated to the Hilbert symbol is Diophantine stable with probability $1$. Our asymptotic formula for the second order term exhibits strong bias towards instability.

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