4 papers
Bateman-Horn, polynomial Chowla and the Hasse principle with probability 1
Tim Browning, Efthymios Sofos, Joni Teräväinen
With probability 1, we assess the average behaviour of various arithmetic functions at the values of degree d polynomials f that are ordered by height. This allows us to establish…
Counting square-free values of random polynomials
Efthymios Sofos
We prove that the average error term when counting square-free values of polynomials is the quartic root of the main term.
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.
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…