scholarly journals Toroidal Automorphic Forms, Waldspurger Periods and Double Dirichlet Series

2012 ◽  
pp. 131-146
Author(s):  
Gunther Cornelissen ◽  
Oliver Lorscheid
Keyword(s):  
Dirichlet Series ◽  
Automorphic Forms ◽  
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.

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