Restriction norms for Siegel Modular Forms
Restriction norms for Siegel Modular Forms
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DissertationDate of Exam
15.08.2024Date of Publication
11.10.2024Advisor
Blomer, ValentinCo-Referee
Fintzen, JessicaMetadata
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Abstract
We consider the L2-norm of Siegel modular forms when restricted to the imaginary axis in an average sense. We establish an asymptotic formula with a power-saving error for cusp forms of degrees 1 and 2 in the weight aspect. We also prove an asymptotic formula for cusp forms of degree 1 in the level aspect. The result are consistent with the Mass Equidistribution Conjecture for Siegel modular forms and the Lindelöf Hypothesis for some twisted Koecher-Maass series. Along the way, we perform a careful analysis of the Kitaoka formula of degree 2. Finally, we prove a non-trivial bound for symplectic Kloosterman sums appearing in the Kitaoka formula of degree 3.
Subjects
automorphe Form, Restriktionsproblem, Spurformeln, quantum unique ergodicity, Exponentialsumme, automorphic form, restriction problem, trace formula, quantum unique ergodicity, exponential sum
Classification (DDC)
510 MathematikRelated Publications
arXiv:2308.13493Felber, Gilles: Restriction norms for Siegel Modular Forms. - Bonn, 2024. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-78843
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-78843
@phdthesis{handle:20.500.11811/12458,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-78843,
author = {{Gilles Felber}},
title = {Restriction norms for Siegel Modular Forms},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2024,
month = oct,
note = {We consider the L2-norm of Siegel modular forms when restricted to the imaginary axis in an average sense. We establish an asymptotic formula with a power-saving error for cusp forms of degrees 1 and 2 in the weight aspect. We also prove an asymptotic formula for cusp forms of degree 1 in the level aspect. The result are consistent with the Mass Equidistribution Conjecture for Siegel modular forms and the Lindelöf Hypothesis for some twisted Koecher-Maass series. Along the way, we perform a careful analysis of the Kitaoka formula of degree 2. Finally, we prove a non-trivial bound for symplectic Kloosterman sums appearing in the Kitaoka formula of degree 3.},
url = {https://hdl.handle.net/20.500.11811/12458}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-78843,
author = {{Gilles Felber}},
title = {Restriction norms for Siegel Modular Forms},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2024,
month = oct,
note = {We consider the L2-norm of Siegel modular forms when restricted to the imaginary axis in an average sense. We establish an asymptotic formula with a power-saving error for cusp forms of degrees 1 and 2 in the weight aspect. We also prove an asymptotic formula for cusp forms of degree 1 in the level aspect. The result are consistent with the Mass Equidistribution Conjecture for Siegel modular forms and the Lindelöf Hypothesis for some twisted Koecher-Maass series. Along the way, we perform a careful analysis of the Kitaoka formula of degree 2. Finally, we prove a non-trivial bound for symplectic Kloosterman sums appearing in the Kitaoka formula of degree 3.},
url = {https://hdl.handle.net/20.500.11811/12458}
}
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