Double Dirichlet series and the n -th order twists of Hecke L -series

2003 ◽  
Vol 327 (2) ◽  
pp. 315-338 ◽  
Author(s):  
Solomon Friedberg ◽  
Jeffrey Hoffstein ◽  
Daniel Lieman
Keyword(s):  
Dirichlet Series ◽  
Double Dirichlet Series

scholarly journals The Growth on the Maximum Modulus of Double Dirichlet Series

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yong-Qin Cui ◽  
Hong-Yan Xu ◽  
Na Li
Keyword(s):  
Dirichlet Series ◽  
Partial Derivative ◽  
Entire Functions ◽  
Maximum Modulus ◽  
Logarithmic Order ◽  
Double Dirichlet Series

The main purpose of this paper is to investigate the growth of several entire functions represented by double Dirichlet series of finite logarithmic order, h-order. Besides, we also study some properties on the maximum modulus of double Dirichlet series and its partial derivative. Our results are extension and improvement of previous results given by Huo and Liang.

scholarly journals Subconvexity for a double Dirichlet series

2010 ◽  
Vol 147 (2) ◽  
pp. 355-374 ◽  
Author(s):  
Valentin Blomer
Keyword(s):  
Dirichlet Series ◽  
Functional Equations ◽  
Mean Square ◽  
Double Dirichlet Series ◽  
Image Position

AbstractFor two real characters ψ,ψ′ of conductor dividing 8 define where $\chi _d = (\frac {d}{.})$ and the subscript 2 denotes the fact that the Euler factor at 2 has been removed. These double Dirichlet series can be extended to $\Bbb {C}^2$ 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.

scholarly journals Composition operators on spaces of double Dirichlet series

2020 ◽  
Author(s):  
Frédéric Bayart ◽  
Jaime Castillo-Medina ◽  
Domingo García ◽  
Manuel Maestre ◽  
Pablo Sevilla-Peris
Keyword(s):  
Dirichlet Series ◽  
Composition Operators ◽  
Double Dirichlet Series

scholarly journals Subconvexity for a double Dirichlet series and non-vanishing of L-functions

2018 ◽  
Vol 14 (06) ◽  
pp. 1573-1604
Author(s):  
Alexander Dahl
Keyword(s):  
Functional Equation ◽  
Positive Integer ◽  
Dirichlet Series ◽  
Upper Bound ◽  
Dihedral Group ◽  
Central Point ◽  
Double Dirichlet Series ◽  
Dirichlet Characters ◽  
Equation Group

We study a double Dirichlet series of the form [Formula: see text], where [Formula: see text] and [Formula: see text] are quadratic Dirichlet characters with prime conductors [Formula: see text] and [Formula: see text] respectively. A functional equation group isomorphic to the dihedral group of order 6 continues the function meromorphically to [Formula: see text]. The developed theory is used to prove an upper bound for the smallest positive integer [Formula: see text] such that [Formula: see text] does not vanish. Additionally, a convexity bound at the central point is established to be [Formula: see text] and a subconvexity bound of [Formula: see text] is proven. An application of bounds at the central point to the non-vanishing problem is also discussed.

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