eng
episciences.org
Hardy-Ramanujan Journal
2804-7370
2019-01-23
10.46298/hrj.2019.5110
5110
journal article
On certain sums over ordinates of zeta-zeros II
Andriy Bondarenko
Aleksandar Ivić
Eero Saksman
Kristian Seip
Let γ denote the imaginary parts of complex zeros ρ = β + iγ of ζ(s). The problem of analytic continuation of the function $G(s) :=\sum_{\gamma >0} {\gamma}^{-s}$ to the left of the line $\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 in [Iv01].
https://hrj.episciences.org/5110/pdf
2010 Mathematics Subject Classification 11M06 Keywords Riemann zeta-function
Riemann hypothesis
analytic continuation
Laurent expansion
second moment
[ MATH ] Mathematics [math]
[ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT]