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Subconvexity for a double Dirichlet series

Published online by Cambridge University Press:  07 September 2010

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

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.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2010

References

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