Complex zeros of real ergodic eigenfunctions

Steve Zelditch*

*Corresponding author for this work

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

We determine the limit distribution (as λ→∞) of complex zeros for holomorphic continuations φCλ toGrauert tubes of real eigenfunctions of the Laplacian on a real analytic compact Riemannian manifold (M, g) with ergodic geodesic flow. If {φjk} is an ergodic sequence of eigenfunctions, we prove the weak limit formula the current of integration over the complex zeros and where ∂ is with respect to the adapted complex structure of Lempert-Szöke and Guillemin-Stenzel.

Original languageEnglish (US)
Pages (from-to)419-443
Number of pages25
JournalInventiones Mathematicae
Volume167
Issue number2
DOIs
StatePublished - Jan 1 2007

ASJC Scopus subject areas

  • Mathematics(all)

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