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Subconvexity for a double Dirichlet series

Part of: Exponential sums and character sums Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  07 September 2010

Valentin Blomer
Valentin Blomer*
Affiliation:
Mathematisches Institut, Bunsenstrasse 3–5, 37073 Göttingen, Germany (email: blomer@uni-math.gwdg.de)
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Abstract

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For two real characters ψ,ψ′ of conductor dividing 8 define where and the subscript 2 denotes the fact that the Euler factor at 2 has been removed. These double Dirichlet series can be extended to possessing a group of functional equations isomorphic to D12. The convexity bound for Z(s,w;ψ,ψ′) is |sw(s+w)|1/4+ε for ℜs=ℜw=1/2. It is proved that Moreover, the following mean square Lindelöf-type bound holds: for any Y1,Y2≥1.

Keywords

multiple Dirichlet seriessubconvexityfunctional equationcharacter sums

MSC classification

Secondary: 11M41: Other Dirichlet series and zeta functions 11L40: Estimates on character sums
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 2 , March 2011 , pp. 355 - 374
Copyright
Copyright © Foundation Compositio Mathematica 2010

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