Intertwining periods, L-functions and local-global principles for distinction of automorphic representations
Abstract
We provide a criterion for non-vanishing of period integrals on automorphic representations of a general linear group over a division algebra. We consider three different periods: linear periods, twisted-linear periods and Galois periods. Our criterion is a local-global principle, which is stated in terms of local distinction, a further local obstruction, and poles of certain global L-functions associated to the underlying involution via the Jacquet-Langlands correspondence. Our local-global principle follows from a new method, relying on the Maass-Selberg relations and a careful analysis of singularities of local and global intertwining periods. Our results generalize to inner forms, known results for split general linear groups. Moreover, our result for twisted linear periods is new even in the split situation. As a consequence of our local-global principle, we complete the proof of one direction of the Guo-Jacquet conjecture.
Keywords
Cite
@article{arxiv.2509.00441,
title = {Intertwining periods, L-functions and local-global principles for distinction of automorphic representations},
author = {Nadir Matringe and Omer Offen and Chang Yang},
journal= {arXiv preprint arXiv:2509.00441},
year = {2026}
}
Comments
We highlighted the main results in the introduction, including the main local result. We also expanded the statement of our main theorem in the case of linear periods, which takes the same form as our main theorem in the Galois case