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arXiv · 2111.09923

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

Radu Toma
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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 $\operatorname{SL}_p(\mathbb{R})/\operatorname{SO}(p)$ 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.

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Radu Toma. 2021-11-18. Hybrid bounds for the sup-norm of automorphic forms in higher rank. https://doi.org/10.1090/tran%2F8921

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