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A225961 Decimal expansion of the position of a minimum of Arias de Reyna and van de Lune's kappa function. 1
7, 7, 9, 8, 5, 3, 5, 7, 5, 3, 3, 8, 8, 3, 6, 0, 3, 0, 5, 1, 8, 2, 0, 9, 2, 0, 8, 1, 2, 2, 5, 3, 7, 1, 0, 7, 1, 8, 5, 6, 7, 3, 2, 7, 6, 8, 0, 7, 4, 0, 3, 8, 6, 2, 6, 7, 0, 0, 2, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The kappa function is implicitly defined by exp(2*pi*i*kappa(t)) = -exp(-2*i*theta(t))*(zeta'(1/2-i*t)/zeta'(1/2+i*t)) and kappa(0)=-1/2.

LINKS

Table of n, a(n) for n=0..59.

J. Arias de Reyna and J. van de Lune, On the exact location of the non-trivial zeros of Riemann's zeta function, arXiv:1305.3844 [math.NT].

EXAMPLE

0.779853575338836030518209208122537107185673276807403862670020...

MATHEMATICA

kappa[t_] := -1 - 1/Pi*Arg[ RiemannSiegelZ'[t] - I*RiemannSiegelZ[t]*RiemannSiegelTheta'[t]]; digits = 60; t0[n_] := t0[n] = (t /. FindMinimum[kappa[t], {t, 1}, WorkingPrecision -> n] [[2]]) // RealDigits[#, 10, digits] & // First; t0[digits]; t0[n = 2*digits]; While[t0[n] != t0[n - digits], n = n + digits]; t0[n]

CROSSREFS

Cf. A114866, A225962 (value of minimum).

Sequence in context: A335847 A244649 A267040 * A099290 A224895 A103569

Adjacent sequences:  A225958 A225959 A225960 * A225962 A225963 A225964

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, May 22 2013

STATUS

approved

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Last modified January 18 09:26 EST 2022. Contains 350454 sequences. (Running on oeis4.)