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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 30, Issue 5


Upper bounds for geodesic periods over rank one locally symmetric spaces

Jan FrahmORCID iD: http://orcid.org/0000-0003-4174-5933 / Feng SuORCID iD: http://orcid.org/0000-0002-4867-5897
Published Online: 2018-01-13 | DOI: https://doi.org/10.1515/forum-2017-0185


We prove upper bounds for geodesic periods of automorphic forms over general rank one locally symmetric spaces. Such periods are integrals of automorphic forms restricted to special totally geodesic cycles of the ambient manifold and twisted with automorphic forms on the cycles. The upper bounds are in terms of the Laplace eigenvalues of the two automorphic forms, and they generalize previous results for real hyperbolic manifolds to the context of all rank one locally symmetric spaces.

Keywords: Locally symmetric spaces; automorphic forms; geodesic periods; totally geodesic cycles; unitary representations; reductive Lie groups

MSC 2010: 11F70; 22E46; 53C35


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About the article

Received: 2017-09-04

Revised: 2017-11-29

Published Online: 2018-01-13

Published in Print: 2018-09-01

Citation Information: Forum Mathematicum, Volume 30, Issue 5, Pages 1065–1077, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0185.

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