Hybrid bounds for the sup-norm of automorphic forms in higher rank
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- by Radu Toma
- Trans. Amer. Math. Soc. 376 (2023), 5573-5600
- DOI: https://doi.org/10.1090/tran/8921
- Published electronically: May 19, 2023
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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.References
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Bibliographic Information
- Radu Toma
- Affiliation: Mathematisches Institut, Endenicher Allee 60, 53115 Bonn, Germany
- MR Author ID: 1380175
- ORCID: 0000-0002-4899-7095
- Email: toma@math.uni-bonn.de
- Received by editor(s): April 13, 2022
- Received by editor(s) in revised form: January 5, 2023
- Published electronically: May 19, 2023
- Additional Notes: The author was supported by Germany Excellence Strategy grant EXC-2047/1-390685813 through the Bonn International Graduate School of Mathematics
- © Copyright 2023 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 376 (2023), 5573-5600
- MSC (2020): Primary 11F55, 11F72, 11D45, 11R52
- DOI: https://doi.org/10.1090/tran/8921
- MathSciNet review: 4630754