A Gelfand–Beurling Type Formula for Heights on Endomorphism Rings Original Research Article

Let V be a finite-dimensional vector space over a number field. In this paper we prove a limit formula for heights on the endomorphism ring of V, which can be considered as the analogue for both the Gelfand–Beurling formula for the spectral radius on a Banach algebra and Tateʹs averaging procedure for constructing canonical heights on abelian varieties. We also prove a version of Northcottʹs finiteness theorem.