2023/08/14 by Schefer, Gerold
#11R06 (Primary) 11G50 (Secondary) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2308.06990
For every algebraic number κ on the unit circle which is not a root of unity we prove the existence of a strict sequence of algebraic numbers whose height tends to zero, such that the averages of the evaluation of fκ(z)=log|z -κ| in the conjugates are essentially bounded from above by -h(κ). This completes a characterisation on functions fκ initiated by Autissier and Baker-Masser, who cover the cases κ=2 and |κ|≠ 1 respectively. Using the same ideas we also prove analogues in the p-adic setting.