Salem Numbers and the Spectrum of Hyperbolic Surfaces

DOI10.1093/IMRN/RNY225zbMATH Open1468.11220arXiv1612.05935OpenAlexW2950352404WikidataQ129264897 ScholiaQ129264897MaRDI QIDQ5854220

Emmanuel Breuillard, Bertrand Deroin

Publication date: 16 March 2021

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: We give a reformulation of Salem's conjecture about the absence of Salem numbers near one in terms of a uniform spectral gap for certain arithmetic hyperbolic surfaces.

Full work available at URL: https://arxiv.org/abs/1612.05935

zbMATH Keywords

automorphic formsSalem numbersCheeger constanteigenvalues of Laplacianlength of geodesicsarithmetic orbifolds

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06)

Related Items (6)

Salem numbers and automorphisms of complex surfaces ⋮ Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups ⋮ Bottom of the length spectrum of arithmetic orbifolds ⋮ Unnamed Item ⋮ Density of systoles of hyperbolic manifolds ⋮ Salem numbers and arithmetic hyperbolic groups

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