Article contents
Hybrid bounds for automorphic forms on ellipsoids over number fields
Published online by Cambridge University Press: 20 December 2012
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 } $.
Keywords
MSC classification
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 12 , Issue 4 , October 2013 , pp. 727 - 758
- Copyright
- ©Cambridge University Press 2012
References
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