Zeta zeros, Hurwitz zeta functions and L(1,\(\chi\) ) (Q1262337)

Assuming the Riemann Hypothesis for \(\zeta (s)=\sum_{n\geq 1}n^{-s}\), the author evaluates the limit \(\lim_{T\to \infty}T^{- 1}\sum_{0<\gamma \leq T}\zeta (+i\gamma,a),\) where \(\gamma\) ranges over the imaginary parts of the zeros of \(\zeta\) (s); here \(\zeta (s,a)=\sum_{n\geq 1}(n+a)^{-s}\) is the Hurwitz zeta-function. In the course of this consideration, the author makes use of his previous work [cf. Comment. Math. Univ. St. Pauli 31, 99-113 (1982; Zbl 0489.10032), and Proc. Japan Acad., Ser. A 63, 370-373 (1987; Zbl 0636.10032)].