Abstract
Let H j ( s) be the Hecke L-function attached to the Maass wave form for the jth eigenvalue 1 4 +κ j 2 of the hyperbolic Laplacian acting in the Hilbert space of automorphic functions for the full modular group. The following mean value estimate for the central values H j( 1 2 ) is proved: ∑ κ j⩽K H j 12 1 2 ⪡K 4+ε.
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