Hardy Ramanujan Journal |

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].

Source : oai:HAL:hal-01986703v1

Published on: January 23, 2019

Submitted on: January 23, 2019

Keywords: 2010 Mathematics Subject Classification 11M06 Keywords Riemann zeta-function,Riemann hypothesis,analytic continuation,Laurent expansion,second moment,
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MATH
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Mathematics [math],
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MATH.MATH-NT
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Mathematics [math]/Number Theory [math.NT]