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A333360 Decimal expansion of Sum_{n>=1} 1/z(n)^3 where z(n) is the imaginary part of the n-th nontrivial zero of the Riemann zeta function. 4
0, 0, 0, 7, 2, 9, 5, 4, 8, 2, 7, 2, 7, 0, 9, 7, 0, 4, 2, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(1)-a(7) published by André Voros in 2001.

a(8)-a(20) computed by David Platt, Mar 15 2020.

Sum_{m>=1} 1/z(m) is a divergent series; see A332614.

Sum_{m>=1} 1/z(m)^2 = 0.0231049931...; see A332645.

Sum_{m>=1} 1/(1/4 + z(m)^2) = 0.023095708966...; see A074760.

Sum_{m>=1} 1/(1/2 + i*z(m))^2 + 1/(1/2 - i*z(m))^2 = -0.046154317...; see A245275.

Sum_{m>=1} 1/(1/2 + i*z(m))^3 + 1/(1/2 - i*z(m))^3 = -0.00011115823...; see A245276.

LINKS

Table of n, a(n) for n=0..19.

André Voros, Zeta functions for the Riemann zeros, arXiv:math/0104051 [math.CV], 2002-2003, p. 25 Table 2.

André Voros, Zeta functions for the Riemann zeros, 2001(2008) p. 20 Table 1.

André Voros,Zeta functions for the Riemann zeros, Annales de l'Institut Fourier, Tome 53 (2003) no. 3, pp. 665-699.

FORMULA

No explicit formula is known (Andre Voros, personal communication to Artur Jasinski, Mar 09 2020).

EXAMPLE

0.00072954827270970421...

CROSSREFS

Cf. A013629, A074760, A104539, A104540, A104541, A104542, A245275, A245276, A306339, A306340, A306341, A332645.

Sequence in context: A021987 A031026 A216186 * A021936 A277525 A154176

Adjacent sequences:  A333357 A333358 A333359 * A333361 A333362 A333363

KEYWORD

nonn,cons,more

AUTHOR

Artur Jasinski, Mar 16 2020

STATUS

approved

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Last modified August 15 16:02 EDT 2020. Contains 336505 sequences. (Running on oeis4.)