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Hybrid bounds for automorphic forms on ellipsoids over number fields

Published online by Cambridge University Press:  20 December 2012

Valentin Blomer
Affiliation:
Mathematisches Institut, Universität Göttingen, Bunsenstr. 3-5, 37073 Göttingen, Germany (blomer@uni-math.gwdg.de)
Philippe Michel
Affiliation:
EPFL/SB/IMB/TAN, Station 8, CH-1015 Lausanne, Switzerland (philippe.michel@epfl.ch)
Corresponding

Abstract

We prove upper bounds for Hecke–Laplace eigenfunctions on certain Riemannian manifolds $X$ of arithmetic type, uniformly in the eigenvalue and the volume of the manifold. The manifolds under consideration are $d$ -fold products of $2$ -spheres or $3$ -spheres, realized as adelic quotients of quaternion algebras over totally real number fields. In the volume aspect we prove a (‘Weyl-type’) saving of $\mathrm{vol} \hspace{0.167em} (X)^{- 1/ 6+ \varepsilon } $ .

Type
Research Article
Copyright
©Cambridge University Press 2012 

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