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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

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 27, Issue 3


A uniform bound for geodesic periods of eigenfunctions on hyperbolic surfaces

Andre Reznikov
Published Online: 2013-04-25 | DOI: https://doi.org/10.1515/forum-2012-0185


We consider periods along closed geodesics and along geodesic circles for eigenfunctions of the Laplace–Beltrami operator on a compact hyperbolic Riemann surface. We obtain uniform bounds for such periods as the corresponding eigenvalue tends to infinity. We use methods from the theory of automorphic functions and, in particular, the uniqueness of the corresponding invariant functionals on irreducible unitary representations of PGL2(ℝ).

Keywords: Eigenfunctions; Laplace operator; periods; hyperbolic surfaces

MSC: 35P15; 11F70

About the article

Received: 2012-12-25

Revised: 2013-03-06

Published Online: 2013-04-25

Published in Print: 2015-05-01

Funding Source: BSF

Funding Source: Excellency Center of the Israel Science Foundation

Award identifier / Grant number: 1691/10

Funding Source: Emmy Noether Institute for Mathematics (the Center of Minerva Foundation of Germany)

Funding Source: ERC

Award identifier / Grant number: 291612

Citation Information: Forum Mathematicum, Volume 27, Issue 3, Pages 1569–1590, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0185.

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