Subconvexity for a double Dirichlet series
2011 | journal article. A publication with affiliation to the University of Göttingen.
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- Authors
- Blomer, Valentin
- Abstract
- For two real characters ; 0 of conductor dividing 8 de ne Z(s; w; ; 0) := 2(2s + 2w 1) X d odd L2(s; d ) 0(d) dw where d = ( d : ) and the subscript 2 denotes the fact that the Euler factor at 2 has been removed. These double Dirichlet series can be extended to C2 possessing a group of functional equations isomorphic to D12. The convexity bound for Z(s; w; ; 0) is jsw(s + w)j1=4+" for <s = <w = 1=2. It is proved that Z(s; w; ; 0) jsw(s + w)j1=6+"; <s = <w = 1=2: Moreover, the following mean square Lindel of-type bound holds: Z Y1 Y1 Z Y2 Y2 jZ(1=2 + it; 1=2 + iu; ; 0)j2 du dt (Y1Y2)1+"; for any Y1; Y2 > 1.
- Issue Date
- 2011
- Publisher
- Oxford University Press (OUP)
- Journal
- Compositio Mathematica
- Organization
- Fakultät für Mathematik und Informatik
- ISSN
- 1570-5846; 0010-437X
- Language
- English