A175642 Decimal expansion of the negated Dirichlet Prime L-function of the real non-principal character mod 5 at 1.
1, 0, 0, 7, 9, 9, 6, 5, 4, 7, 9, 3, 9, 8, 6, 1, 1, 7, 2, 2, 6, 1, 6, 6, 6, 0, 7, 5, 5, 1, 2, 6, 7, 8, 5, 6, 6, 9, 9, 9, 0, 3, 1, 9, 5, 6, 6, 4, 9, 3, 2, 7, 0, 9, 7, 1, 6, 3, 7, 4, 5, 5, 3, 9, 5, 0, 0, 1, 4, 9, 4, 5, 8, 8, 5, 3, 9, 3, 2, 4, 8, 6, 4, 3, 3, 8, 6, 8, 1, 3, 3, 8, 6, 3, 3, 7, 3, 8, 2, 7, 2, 3, 7, 6, 2
Offset: 1
Examples
S(1,chi_3) = -1.0079965479398611722616660755126785669990319566493...
Links
- R. J. Mathar, Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015.
Programs
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Mathematica
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[5, 3, 1], digits]], 10, digits-1][[1]] (* Vaclav Kotesovec, Jan 22 2021 *)
Extensions
More digits from Vaclav Kotesovec, Jan 22 2021
Comments