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THE MAXIMAL GROWTH OF TORIC PERIODS AND OSCILLATORY INTEGRALS FOR MAXIMAL FLAT SUBMANIFOLDS

Abstract : We prove a new omega result for toric periods of Hecke-Maass forms on compact locally symmetric spaces associated to forms of PGL(3). This is motivated by conjectures on the maximal growth of L-functions as well as by questions about the size of automorphic periods. We also prove a mean square asymptotic result for maximal flat periods on more general locally symmetric spaces of non-compact type, which takes as main input bounds for real relative orbital integrals.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03695051
Contributor : Bart Michels Connect in order to contact the contributor
Submitted on : Tuesday, June 14, 2022 - 2:00:32 PM
Last modification on : Saturday, June 25, 2022 - 3:43:19 AM

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  • HAL Id : hal-03695051, version 1
  • ARXIV : 2206.07409

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Bart Michels. THE MAXIMAL GROWTH OF TORIC PERIODS AND OSCILLATORY INTEGRALS FOR MAXIMAL FLAT SUBMANIFOLDS. 2022. ⟨hal-03695051⟩

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