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Double Dirichlet series
and quantum unique ergodicity of weight one-half Eisenstein
series
Yiannis N. Petridis, Nicole Raulf and Morten S. Risager |
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Vol. 8 (2014), No. 7, 1539–1595
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Abstract |
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The problem of quantum unique ergodicity (QUE) of weight Eisenstein series for leads to the study of certain double Dirichlet series involving automorphic forms and Dirichlet characters. We study the analytic properties of this family of double Dirichlet series (analytic continuation, convexity estimate) and prove that a subconvex estimate implies the QUE result. |
Keywords
quantum limits, Eisenstein series, multiple Dirichlet
series.
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Mathematical Subject Classification 2010
Primary: 58J51
Secondary: 11F68, 11F72
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Milestones
Received: 5 October 2012
Revised: 3 August 2014
Accepted: 8 September 2014
Published: 21 October 2014
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Authors |
| Yiannis N. Petridis | |
| Department of Mathematics University College London Gower street London WC1E 6BT United Kingdom |
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| Nicole Raulf | |
| Laboratoire Paul Painlevé U.F.R. de Mathématiques Université Lille 1 Sciences et Technologies 59 655 Villeneuve d’Asqc Cédex France |
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| Morten S. Risager | |
| Department of Mathematical
Sciences University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen Ø Denmark |
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