Upper bounds for geodesic periods over rank one locally symmetric spaces

Jan Frahm; Feng Su

doi:10.1515/forum-2017-0185

Upper bounds for geodesic periods over rank one locally symmetric spaces

Jan Frahm, Feng Su

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1065-1077
Number of pages	13
Journal	Forum Mathematicum
Volume	30
Issue number	5
DOIs	https://doi.org/10.1515/forum-2017-0185
State	Published - 1 Sep 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018 Walter de Gruyter GmbH, Berlin/Boston.

Keywords

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

Access to Document

10.1515/forum-2017-0185

Cite this

@article{b0f34d80eb4e4d53ba29ef7c90517b78,

title = "Upper bounds for geodesic periods over rank one locally symmetric spaces",

abstract = "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, reductive Lie groups, totally geodesic cycles, unitary representations",

author = "Jan Frahm and Feng Su",

note = "Publisher Copyright: {\textcopyright} 2018 Walter de Gruyter GmbH, Berlin/Boston.",

year = "2018",

month = sep,

day = "1",

doi = "10.1515/forum-2017-0185",

language = "אנגלית",

volume = "30",

pages = "1065--1077",

journal = "Forum Mathematicum",

issn = "0933-7741",

publisher = "Walter de Gruyter GmbH",

number = "5",

}

TY - JOUR

T1 - Upper bounds for geodesic periods over rank one locally symmetric spaces

AU - Frahm, Jan

AU - Su, Feng

PY - 2018/9/1

Y1 - 2018/9/1

N2 - 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.

AB - 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.

KW - Locally symmetric spaces

KW - automorphic forms

KW - geodesic periods

KW - reductive Lie groups

KW - totally geodesic cycles

KW - unitary representations

UR - http://www.scopus.com/inward/record.url?scp=85041040755&partnerID=8YFLogxK

U2 - 10.1515/forum-2017-0185

DO - 10.1515/forum-2017-0185

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85041040755

SN - 0933-7741

VL - 30

SP - 1065

EP - 1077

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 5

ER -

Upper bounds for geodesic periods over rank one locally symmetric spaces

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this