Quantitative logarithmic equidistribution of the crucial measures

Kenneth S. Jacobs*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let K be an algebraically closed field of characteristic 0 that is complete with respect to a non-Archimedean absolute value, and let ϕ∈ K(z) with deg (ϕ) ≥ 2. Recently, Rumely introduced a family of discrete probability measures {νϕn} on the Berkovich line PK1 over K which carry information about the reduction of conjugates of ϕ. In a previous article, the author showed that the measures νϕn converge weakly to the canonical measure μϕ. In this article, we extend this result to allow test functions which may have logarithmic singularities at the boundary of PK1. These integrands play a key role in potential theory, and we apply our main results to show the potential functions attached to νϕn converge to the potential function attached to μϕ, as well as an approximation result for the Lyapunov exponent of ϕ.

Original languageEnglish (US)
Article number10
JournalResearch in Number Theory
Volume4
Issue number1
DOIs
StatePublished - Mar 1 2018

ASJC Scopus subject areas

  • Algebra and Number Theory

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