The sup-norm problem for automorphic forms in higher rank
The sup-norm problem for automorphic forms in higher rank
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DissertationDate of Exam
16.09.2024Date of Publication
18.09.2024Advisor
Blomer, ValentinCo-Referee
Stroppel, CatharinaMetadata
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Abstract
We study the sup-norm of Hecke-Maaß cusp forms on certain locally symmetric spaces of SLn(ℝ). The latter correspond either to cocompact lattices defined by orders in division algebras, or to the Hecke congruence subgroups of SLn(ℤ), yielding non-compact spaces. The main results are sub-baseline bounds uniform in the volume of the space and, in the compact case, also in the spectral parameter. These bounds are the first of their kind for n > 2. The methods involve a thorough study of level structures in higher rank, including a new reduction theory with level in the non-compact case. This is used to solve the core counting problem by soft, generalisable arguments, based on rigidity principles.
Subjects
automorphic forms, division algebras, reduction theory, geometry of numbers, trace formula, quantum chaos
Classification (DDC)
510 MathematikRelated Publications
arXiv:2401.02741https://doi.org/10.1090/tran/8921
Toma, Radu: The sup-norm problem for automorphic forms in higher rank. - Bonn, 2024. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-78181
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-78181
@phdthesis{handle:20.500.11811/12172,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-78181,
author = {{Radu Toma}},
title = {The sup-norm problem for automorphic forms in higher rank},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2024,
month = sep,
note = {We study the sup-norm of Hecke-Maaß cusp forms on certain locally symmetric spaces of SLn(ℝ). The latter correspond either to cocompact lattices defined by orders in division algebras, or to the Hecke congruence subgroups of SLn(ℤ), yielding non-compact spaces. The main results are sub-baseline bounds uniform in the volume of the space and, in the compact case, also in the spectral parameter. These bounds are the first of their kind for n > 2. The methods involve a thorough study of level structures in higher rank, including a new reduction theory with level in the non-compact case. This is used to solve the core counting problem by soft, generalisable arguments, based on rigidity principles.},
url = {https://hdl.handle.net/20.500.11811/12172}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-78181,
author = {{Radu Toma}},
title = {The sup-norm problem for automorphic forms in higher rank},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2024,
month = sep,
note = {We study the sup-norm of Hecke-Maaß cusp forms on certain locally symmetric spaces of SLn(ℝ). The latter correspond either to cocompact lattices defined by orders in division algebras, or to the Hecke congruence subgroups of SLn(ℤ), yielding non-compact spaces. The main results are sub-baseline bounds uniform in the volume of the space and, in the compact case, also in the spectral parameter. These bounds are the first of their kind for n > 2. The methods involve a thorough study of level structures in higher rank, including a new reduction theory with level in the non-compact case. This is used to solve the core counting problem by soft, generalisable arguments, based on rigidity principles.},
url = {https://hdl.handle.net/20.500.11811/12172}
}
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