VALUES OF L-FUNCTIONS AT THE CRITICAL-POINT

For a discriminant D of a binary quadratic form, we study the average value of L(S, E(D)) at the critical point 1/2 where E(D) is defined by W. Kohnen and D. Zagier: [GRAPHICS] for n epsilon N and D = D-0 delta(2), D-0 a fundamental discriminant and delta epsilon N. When D = D-0, L(S, E(D0)) is the Dirichlet series L(S, (D-0/.)). We derive an asymptotic formula for Sigma(D) L(1/2, E(D)), where the sum runs over all discriminants D epsilon (0, Y] or [-Y, 0).