A348562 - OEIS

A348562

Decimal expansion of a limit related to the sum of reciprocals of the imaginary part of the nontrivial zeros of the Riemann zeta function (negated).

1, 7, 1, 5, 9, 4, 0, 4, 3, 0, 7, 0, 9, 8, 1, 4, 9, 4, 5, 4, 1, 9, 1, 6, 1, 4, 2, 7, 3, 9, 6, 4, 2, 9, 2, 6, 1, 5, 3, 6, 0, 1, 1, 1, 7, 4, 8, 1, 8, 3, 5, 9, 1, 2, 1, 5, 1, 5, 9, 1, 2, 5, 1, 3, 7, 0, 6, 7, 8, 2, 4, 4, 5, 8, 1, 5, 1, 4, 0, 6, 7, 7, 9, 8, 1, 9, 1, 7, 5, 7, 2, 8, 1, 5, 9, 8, 5, 3, 4, 3, 3, 3, 7, 8, 4, 4

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OFFSET

-1,2

LINKS

Table of n, a(n) for n=-1..104.

Richard P. Brent, David J. Platt, and Timothy S. Trudgian, A harmonic sum over nontrivial zeros of the Riemann zeta-function, Bulletin of the Australian Mathematical Society, Vol. 104, No. 1 (2021), pp. 59-65; arXiv preprint, arXiv:2009.05251 [math.NT], 2020.

Artur Kawalec, On the series expansion of the secondary zeta function, arXiv:2403.15741 [math.NT], 2024; formula (70).

Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros.

FORMULA

Equals -lim_{T->oo} (Sum_{0 < gamma <= T} 1/gamma) - log(T/(2*Pi))^2/(4*Pi), where gamma denotes the imaginary part of the nontrivial zeros of the Riemann zeta function where multiple zeros (if they exist) are weighted according to their multiplicity.

EXAMPLE

-0.0171594043070981...

CROSSREFS

Cf. A058303, A074760.

Sequence in context: A376841 A195369 A367710 * A047875 A346610 A064467

Adjacent sequences: A348559 A348560 A348561 * A348563 A348564 A348565

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Oct 22 2021

EXTENSIONS

More terms from Artur Jasinski, Apr 06 2024

STATUS

approved