Hybrid bounds for automorphic forms on ellipsoids over number fields

Abstract

We prove upper bounds for Hecke-Laplace eigenfunctions on certain Riemannian manifolds of arithmetic type. 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.

somewhat expanded version, to appear in J. Inst. Math. Jussieu

References in corpus (1)

• Bounding sup-norms of cusp forms of large level

Cited by in corpus (5)

• Bounds for eigenforms on arithmetic hyperbolic 3-manifolds
• Theta functions, fourth moments of eigenforms, and the sup-norm problem II
• Theta functions, fourth moments of eigenforms, and the sup-norm problem I
• Zeroes of quaternionic modular forms and central $L$-values
• Hybrid bounds for the sup-norm of automorphic forms in higher rank