PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.)Vol. 76(90), pp. 41–55 (2004)
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PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.) Vol. 76(90), pp. 41–55 (2004) |
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THE SPECTRAL MEAN SQUARE OF HECKE $L$-FUNCTIONS ON THE CRITICAL LINEM. JutilaDepartment of Mathematics, University of Turku, FIN-20014 Turku, FinlandAbstract: 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. Keywords: automorphic $L$-functions, spectral theory Classification (MSC2000): 11F66; 11M41 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 17 Dec 2004. This page was last modified: 9 Feb 2005.
© 2004 Mathematical Institute of the Serbian Academy of Science and Arts
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