## On certain sums over ordinates of zeta-zeros. II.(English)Zbl 1447.11092

Summary: Let $$\gamma$$ denote the imaginary parts of complex zeros $$\rho=\beta+ i\gamma$$ of $$\zeta(s)$$. The problem of analytic continuation of the function $$G(s):=\sum_{\gamma >0} \gamma^{-s}$$ to the left of the line $$\operatorname{Re} s = -1$$ is investigated, and its Laurent expansion at the pole $$s=1$$ is obtained. Estimates for the second moment on the critical line $$\int_1^T |G(\frac{1}{2}+ it)|^2 dt$$ are revisited. This paper is a continuation of work begun by the second author [Bull., Cl. Sci. Math. Nat., Sci. Math. 122, No. 26, 39–52 (2001; Zbl 0999.11048)].

### MSC:

 11M06 $$\zeta (s)$$ and $$L(s, \chi)$$

Zbl 0999.11048
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