Complex Zeros of Real Ergodic Eigenfunctions
نویسنده
چکیده
We determine the limit distribution (as λ → ∞) of complex zeros for holomorphic continuations φCλ to Grauert 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 1 λj φjk ] → i π∂∂|ξ|g, where φjk ] is the current of integration over the complex zeros and where ∂ is with respect to the adapted complex structure of Lempert-Szöke and Guillemin-Stenzel.
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