Hybrid bounds for the sup-norm of automorphic forms in higher rank

Abstract

Let $A$ be a central division algebra of prime degree $p$ over $\mathbb{Q}$. We obtain subconvex hybrid bounds, uniform in both the eigenvalue and the discriminant, for the sup-norm of Hecke-Maass forms on the compact quotients of ${\mathrm{SL}}_p(\mathbb{R})/\mathrm{SO}(p)$ by unit groups of orders in $A$. The exponents in the bounds are explicit and polynomial in $p$. We also prove subconvex hybrid bounds in the case of certain Eichler-type orders in division algebras of arbitrary odd degree.

arXiv comment29 pages. Minor improvements, implemented suggestions from referee. To appear in Trans. AMS. Comments are welcome!

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Cited by in corpus (1)

• Theta functions, fourth moments of eigenforms, and the sup-norm problem II