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math.NT2025
On the application of large deviation estimates to local solubility in families of varieties
Sun Woo Park, Efthymios Sofos
We apply the Gärtner--Ellis theorem on large deviations to prove a weak version of the Loughran--Smeets conjecture for general fibrations.
math.NT2025
Local solubility in generalised Châtelet varieties
Kevin Destagnol, Julian Lyczak, Efthymios Sofos
We obtain asymptotic formulas for averages of general multivariate arithmetic functions evaluated at polynomial arguments using recent work of Rydin Myerson and Rome-Yamagishi. We…