A225961 Decimal expansion of the position of a minimum of Arias de Reyna and van de Lune's kappa function.

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

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], 2013.

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,more

Author

Jean-François Alcover, May 22 2013

Status

approved