Meromorphic continuation of 𝐿-functions

2009 ◽  
pp. 145-146
Keyword(s):  
Meromorphic Continuation

Fundamental Solutions of Kohn Sub-Laplacians on Anisotropic Heisenberg Groups and H-type Groups

2011 ◽  
Vol 54 (1) ◽  
pp. 126-140 ◽  
Author(s):  
Yongyang Jin ◽  
Genkai Zhang
Keyword(s):  
Fundamental Solutions ◽  
Meromorphic Continuation ◽  
Heisenberg Groups ◽  
Tempered Distributions

AbstractWe prove that the fundamental solutions of Kohn sub-LaplaciansΔ+iα∂t on the anisotropic Heisenberg groups are tempered distributions and have meromorphic continuation in α with simple poles. We compute the residues and find the partial fundamental solutions at the poles. We also find formulas for the fundamental solutions for some matrix-valued Kohn type sub-Laplacians on H-type groups.

Meromorphic Continuation of Spherical Cuspidal Data Eisenstein Series

2007 ◽  
Vol 59 (6) ◽  
pp. 1121-1134 ◽  
Author(s):  
Feryâl Alayont
Keyword(s):  
Eisenstein Series ◽  
Meromorphic Continuation ◽  
Parabolic Subgroups

AbstractMeromorphic continuation of the Eisenstein series induced from spherical, cuspidal data on parabolic subgroups is achieved via reworking Bernstein's adaptation of Selberg's third proof of meromorphic continuation.

Scalar Products of Certain Hecke L-Series and Moments of Weighted Norm-Counting Functions

1985 ◽  
Vol 28 (3) ◽  
pp. 272-279 ◽  
Author(s):  
R. W. K. Odoni
Keyword(s):  
Dirichlet Series ◽  
Finite Groups ◽  
Tensor Products ◽  
Meromorphic Continuation ◽  
Weighted Norm ◽  
Mellin Transformation ◽  
Counting Functions ◽  
Representations Of Finite Groups ◽  
Scalar Products

AbstractWe consider Dirichlet series R(s), constructed by taking scalar products of Hecke L-series with ray-class characters. Using a theorem of G. W. Mackey on tensor products of representations of finite groups we show that R(s) has a meromorphic continuation into Re(s) > 1/2 (obtained by more sophisticated methods in [l]-[5]); we then obtain estimates for the growth of R(s) on vertical lines. Via the Mellin transformation we deduce asymptotics for various weighted moment sums involving ideals of given ray-class and norm, in one or several fields simultaneously.

scholarly journals A Family of Riesz Distributions for Differential Forms on Euclidian Space

2020 ◽  
Author(s):  
Matthias Fischmann ◽  
Bent Ørsted
Keyword(s):  
Fourier Transforms ◽  
Conformal Geometry ◽  
Differential Forms ◽  
Natural Generalization ◽  
Conformal Group ◽  
Meromorphic Continuation ◽  
New Family ◽  
Euclidian Space

Abstract In this paper, we introduce a new family of operator-valued distributions on Euclidian space acting by convolution on differential forms. It provides a natural generalization of the important Riesz distributions acting on functions, where the corresponding operators are $(-\Delta )^{-\alpha /2}$, and we develop basic analogous properties with respect to meromorphic continuation, residues, Fourier transforms, and relations to conformal geometry and representations of the conformal group.

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