Scalar Products of Certain Hecke L-Series and Moments of Weighted Norm-Counting Functions
Canadian mathematical bulletin, Tome 28 (1985) no. 3, pp. 272-279
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We 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.
Odoni, R. W. K. Scalar Products of Certain Hecke L-Series and Moments of Weighted Norm-Counting Functions. Canadian mathematical bulletin, Tome 28 (1985) no. 3, pp. 272-279. doi: 10.4153/CMB-1985-033-4
@article{10_4153_CMB_1985_033_4,
author = {Odoni, R. W. K.},
title = {Scalar {Products} of {Certain} {Hecke} {L-Series} and {Moments} of {Weighted} {Norm-Counting} {Functions}},
journal = {Canadian mathematical bulletin},
pages = {272--279},
year = {1985},
volume = {28},
number = {3},
doi = {10.4153/CMB-1985-033-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-033-4/}
}
TY - JOUR AU - Odoni, R. W. K. TI - Scalar Products of Certain Hecke L-Series and Moments of Weighted Norm-Counting Functions JO - Canadian mathematical bulletin PY - 1985 SP - 272 EP - 279 VL - 28 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-033-4/ DO - 10.4153/CMB-1985-033-4 ID - 10_4153_CMB_1985_033_4 ER -
%0 Journal Article %A Odoni, R. W. K. %T Scalar Products of Certain Hecke L-Series and Moments of Weighted Norm-Counting Functions %J Canadian mathematical bulletin %D 1985 %P 272-279 %V 28 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-033-4/ %R 10.4153/CMB-1985-033-4 %F 10_4153_CMB_1985_033_4
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