Vol. 8, No. 7, 2014

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ISSN: 1944-7833 (e-only)
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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

Vol. 8 (2014), No. 7, 1539–1595
Abstract

The problem of quantum unique ergodicity (QUE) of weight 1 2 Eisenstein series for Γ0(4) leads to the study of certain double Dirichlet series involving GL2 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.
Mathematical Subject Classification 2010
Primary: 58J51
Secondary: 11F68, 11F72
Milestones
Received: 5 October 2012
Revised: 3 August 2014
Accepted: 8 September 2014
Published: 21 October 2014
Authors
Yiannis N. Petridis
Department of Mathematics
University College London
Gower street
London
WC1E 6BT
United Kingdom
Nicole Raulf
Laboratoire Paul Painlevé
U.F.R. de Mathématiques
Université Lille 1
Sciences et Technologies
59 655 Villeneuve d’Asqc Cédex
France
Morten S. Risager
Department of Mathematical Sciences
University of Copenhagen
Universitetsparken 5
DK-2100 Copenhagen Ø
Denmark