\(L^ \infty\)-norms of eigenfunctions for arithmetic hyperbolic 3-manifolds

DOI10.1215/S0012-7094-95-07724-2zbMath0869.11050OpenAlexW1496415642MaRDI QIDQ1896005

Shin-ya Koyama

Publication date: 23 March 1996

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-95-07724-2

zbMATH Keywords

quaternion algebrahyperbolic 2-spacearithmetic hyperbolic 3-manifoldseigenspace of the Laplace-Beltrami-operatornorm-1-group\(L^ \infty\)-norms of eigenfunctions

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (7)

Bounds for eigenforms on arithmetic hyperbolic 3-manifolds ⋮ On sup-norms of cusp forms of powerful level ⋮ Large values of eigenfunctions on arithmetic hyperbolic 3-manifolds ⋮ Average behavior of Fourier coefficients of Maass cusp forms for hyperbolic 3-manifolds ⋮ Estimates of automorphic \(L\)-functions in the discriminant-aspect ⋮ Maximum norms of chaotic quantum eigenstates and random waves ⋮ Prime geodesic theorem in the 3-dimensional hyperbolic space

Cites Work

• The arithmetic and geometry of some hyperbolic three manifolds
• The behaviour of eigenstates of arithmetic hyperbolic manifolds
• \(L^ \infty\) norms of eigenfunctions of arithmetic surfaces
• The spectral function of an elliptic operator
• On the Topography of Maass Waveforms for PSL(2, Z)
• Small eigenvalues of Laplacian for $Γ_{0}(N)$
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