The Distribution of Values of the Hecke L-Functions at 1

Let S₂(q) be the set of primitive forms in the space S₂(Γ₀(q)) of holomorpic Γ₀(q)-cusp forms of weight 2. Let f ∈ S₂(q) and let L_f(S) be the L-function of f(z). It is proved that the set {log L_f(1), f ∈ S₂(q)} has a limit distribution function. The rate of convergence to this limit function is estimated. Bibliography: 10 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 15–32.