10.46298/hrj.2019.5110
https://hrj.episciences.org/5110
Bondarenko , Andriy
Andriy
Bondarenko
Ivić , Aleksandar
Aleksandar
Ivić
Saksman , Eero
Eero
Saksman
Seip , Kristian
Kristian
Seip
On certain sums over ordinates of zeta-zeros II
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].
episciences.org
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]
2019-01-23
2019-01-23
2019-01-23
en
journal article
https://hal.science/hal-01986703v1
2804-7370
https://hrj.episciences.org/5110/pdf
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