Geodesic
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

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1985-033-4
Mots-clés : 12A70, 12A55 
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
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