Hybrid Bounds For Automorphic Forms On Ellipsoids Over Number Fields

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 vol (X)(-1/6+epsilon).


Published in:
Journal Of The Institute Of Mathematics Of Jussieu, 12, 4, 727-758
Year:
2013
Publisher:
Cambridge, Cambridge Univ Press
ISSN:
1474-7480
Keywords:
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 Record created 2013-10-01, last modified 2018-03-17

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