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Sup-norms of Eigenfunctions on Arithmetic Ellipsoids

Blomer, Valentin ; Michel, Philippe

In: International Mathematics Research Notices, 2011, vol. 2011, no. 21, p. 4934-4966

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    Title
    • Sup-norms of Eigenfunctions on Arithmetic Ellipsoids
    Author
    • Blomer, Valentin. Mathematisches Institut, Universität Göttingen, Bunsenstr. 3-5, 37073 Göttingen, Germany
    • Michel, Philippe. EPFL/SB/IMB/TAN, Station 8, CH-1015 Lausanne, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • International Mathematics Research Notices, 2011, vol. 2011, no. 21, p. 4934-4966. Oxford University Press
    Other Version
    Classification
    • Health
    OAI-PMH Identifier
    • oai:doc.rero.ch:298646
    Summary
    Let B be a positive quaternion algebra, and let be an Eichler order. There is associated, in a natural way, a variety the connected components of which are indexed by the ideal classes of and are isomorphic to spheres. This variety is naturally equipped with a Laplace operator and a large family of Hecke operators. For a joint eigenfunction φ of the Hecke algebra and of the Laplace operator with eigenvalue λ, the hybrid sup norm bound for any is shown, where t=(1+λ)1/2 and