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arXiv · 2206.07409

The Maximal Growth Of Toric Periods and Oscillatory Integrals for Maximal Flat Submanifolds

Bart Michels
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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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Bart Michels. 2022-06-15. The Maximal Growth Of Toric Periods and Oscillatory Integrals for Maximal Flat Submanifolds. https://arxiv.org/abs/2206.07409

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