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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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

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