Double Dirichlet series and quantum unique ergodicity of weight one-half Eisenstein series

Yiannis N. Petridis, Nicole Raulf, Morten S. Risager

Type: Article

Publication Date: 2014-10-21

Citations: 5

DOI: https://doi.org/10.2140/ant.2014.8.1539

Abstract

The problem of quantum unique ergodicity (QUE) of weight 1/2 Eisenstein series for Γ_0(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.

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+	Multiplicative Number Theory	1980	H. Davenport
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+	On the Ramanujan Conjecture and Finiteness of Poles for Certain L- Functions	1988	Freydoon Shahidi
+	L-functions with n-th order twists	2011	Valentin Blomer Leo Goldmakher Benoît Louvel
+	Nonvanishing Theorems for Automorphic L-Functions on GL(2)	1995	Solomon Friedberg Jeffrey Hoffstein
+	Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. II	1967	Walter Roelcke
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