OFFSET
0,2
COMMENTS
LINKS
R. J. Mathar, Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015.
EXAMPLE
S(1,chi_2) = -0.14194483853319570866139263972173431667541104401...
MATHEMATICA
Do[Print[N[-Log[4/3]/2 + Sum[Log[(Zeta[2*k + 1, 1/6] - Zeta[2*k + 1, 5/6])^2 / ((2^(4*k + 2) - 1) * (3^(4*k + 2) - 1) * Zeta[4*k + 2])] * MoebiusMu[2*k + 1]/(4*k + 2), {k, 1, m}], 120]], {m, 20, 200, 20}] (* Vaclav Kotesovec, Jun 27 2020 *)
S[m_, n_, s_] := (t = 1; sums = 0; difs = 1; While[Abs[difs] > 10^(-digits - 5) || difs == 0, difs = (MoebiusMu[t]/t) * Log[If[s*t == 1, DirichletL[m, n, s*t], Sum[Zeta[s*t, j/m]*DirichletCharacter[m, n, j]^t, {j, 1, m}]/m^(s*t)]]; sums = sums + difs; t++]; sums); $MaxExtraPrecision = 1000; digits = 121; RealDigits[Chop[N[-S[6, 2, 1], digits]], 10, digits-1][[1]] (* Vaclav Kotesovec, Jan 22 2021 *)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
R. J. Mathar, Aug 01 2010
EXTENSIONS
More terms from Vaclav Kotesovec, Jun 27 2020
STATUS
approved