NONVANISHING OF THE FAMILY OF Γ1(q)-AUTOMORPHIC L-FUNCTIONS AT THE CENTRAL POINT.

We investigate proportion of nonvanishing central values L(f, 1/2) of L-functions associated to the basis of holomorphic modular forms of fixed weight k with respect to Γ1(q), in the limit when q → ∞ along the primes. Motivation is a contrast between Γ0(q) and Γ1(q) families in the sense of underlying harmonic analysis. [ABSTRACT FROM AUTHOR]