Geodesic
The Spectral Mean Square of Hecke L-functions on the Critical Line
Publications de l'Institut Mathématique, _N_S_76 (2004) no. 90, p. 41

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The Hecke $L$-function $H_j(s)$ attached to the $j$th Maass form for the full modular group is estimated in the mean square over a spectral interval for $s=\frac12+it$. As a corollary, we obtain the estimate $H_j(\frac12+it)\ll t^{1/3+\varepsilon}$ for $t\gg\kappa_j^{3/2}$, where $1/4+\kappa_j^2$ is the respective $j$th eigenvalue of the hyperbolic Laplacian. This extends a result due to T. Meurman.
DOI : 10.2298/PIM0476041J
Classification : 11F66 11M41
Keywords: automorphic L-functions, spectral theory 
M. Jutila. The Spectral Mean Square of Hecke L-functions on the Critical Line. Publications de l'Institut Mathématique, _N_S_76 (2004) no. 90, p. 41 . doi: 10.2298/PIM0476041J
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