15 May 2021 On the residue method for period integrals
Aaron Pollack, Chen Wan, Michał Zydor
Author Affiliations +
Duke Math. J. 170(7): 1457-1515 (15 May 2021). DOI: 10.1215/00127094-2020-0078


By applying the residue method for period integrals, we prove identities between period integrals on cuspidal automorphic representations and period integrals on residual representations for seven spherical varieties. Combining this with the Langlands–Shahidi theory for residues of Eisenstein series, for each case, we prove some relations between the period integrals and certain automorphic L-functions. In some cases, we also study the local multiplicity of the spherical varieties.


Download Citation

Aaron Pollack. Chen Wan. Michał Zydor. "On the residue method for period integrals." Duke Math. J. 170 (7) 1457 - 1515, 15 May 2021. https://doi.org/10.1215/00127094-2020-0078


Received: 13 March 2019; Revised: 13 October 2020; Published: 15 May 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.1215/00127094-2020-0078

Primary: 11F67
Secondary: 22E50

Keywords: local multiplicity of spherical varieties , period integrals of automorphic forms , special values of automorphic L-functions

Rights: Copyright © 2021 Duke University Press

Vol.170 • No. 7 • 15 May 2021
Back to Top