Hybrid bounds for automorphic forms on ellipsoids over number fields

DOI10.1017/S1474748012000874zbMath1355.11062arXiv1110.4526OpenAlexW3098125154MaRDI QIDQ2852316

Valentin Blomer, Philippe Michel

Publication date: 8 October 2013

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.4526

zbMATH Keywords

spherical harmonicstrace formulanorm formssup-normsdefinite quaternion algebrashybrid bounds

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (8)

Bounds for eigenforms on arithmetic hyperbolic 3-manifolds ⋮ On sup-norms of cusp forms of powerful level ⋮ Quadratic forms and semiclassical eigenfunction hypothesis for flat tori ⋮ Sup-norm of Hecke-Laplace eigenforms on \(S^3\) ⋮ Hybrid bounds for the sup-norm of automorphic forms in higher rank ⋮ Zeroes of quaternionic modular forms and central \(L\)-values ⋮ On the sup-norm of Maass cusp forms of large level. III ⋮ Subconvex bounds for Hecke-Maass forms on compact arithmetic quotients of semisimple Lie groups

Cites Work

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• Sparse equidistribution problems, period bounds and subconvexity
• Bounding sup-norms of cusp forms of large level
• \(L^ \infty\) norms of eigenfunctions of arithmetic surfaces
• Class group \(L\)-functions
• On the sup-norm of Maass cusp forms of large level

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