Non-vanishing of Maass form L-functions at the central point.

In this paper, we consider the family {Lj(s)}j=1∞ of L-functions associated to an orthonormal basis {uj}j=1∞ of even Hecke-Maass forms for the modular group SL(2,Z) with eigenvalues {λj = κj2 + 1/4}j=1∞. We prove the following effective non-vanishing result: At least 50 % of the central values Lj(1/2) with κj ≤ T do not vanish as T → ∞. Furthermore, we establish effective non-vanishing results in short intervals. [ABSTRACT FROM AUTHOR]