Author

Travis Cunningham

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Preprint Aug 2026

Distribution of zeros of holomorphic functions and resonances in logarithmic regions for Schroedinger operators on Euclidean space

Motivated by scattering theory, this paper proves general results about the distribution of zeros in logarithmic neighborhoods of the real axis for a certain class of functions holomorphic in the closed lower half-plane. We define a new \emph{indicator function} that measures the growth of the holomorphic function alon...

Travis Cunningham · 0 citations

Preprint Sep 2026

Microlocal analysis and spectral gap for complex hyperbolic manifolds

We prove the existence of an essential spectral gap for convex cocompact complex hyperbolic manifolds under the hypothesis that the limit set does not contain a complex circle. We apply an extension to complex hyperbolic manifolds due to Quan of the approach of Vasy to meromorphic continuation of the resolvent. This al...

Travis Cunningham · 0 citations