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

Bart Michels (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Domaines: Théorie des nombres [math.NT]; Théorie spectrale [math.SP]

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