A175641 Decimal expansion of the negated Dirichlet Prime L-function of the non-principal character mod 3 at 2.

2, 7, 4, 7, 0, 5, 2, 0, 8, 2, 8, 5, 5, 1, 8, 4, 8, 6, 2, 8, 9, 5, 7, 7, 8, 9, 8, 1, 6, 0, 8, 6, 0, 6, 3, 0, 0, 9, 9, 9, 4, 5, 0, 9, 8, 8, 2, 2, 2, 4, 7, 6, 4, 9, 4, 7, 8, 7, 3, 0, 6, 8, 6, 7, 4, 7, 5, 1, 7, 1, 8, 1, 7, 6, 9, 7, 1, 2, 9, 0, 5, 3, 5, 9, 9, 5, 8, 0, 8, 5, 2, 5, 4, 9, 6, 1, 6, 3, 0, 7, 9, 2, 2, 0, 5, 4

Offset: 0

Author

R. J. Mathar, Aug 01 2010

Keywords

• cons
• nonn

Comments

The absolute value of S(2,chi_2) = sum_{primes p = A000040} A102283(p)/p^2 = -1/2^2 -1/5^2 +1/7^2 -1/11^2 +1/13^2 -1/17^2 +...

Examples

			S(2,chi_2) = -0.274705208285518486289577898160860630099...
		

Links

• R. J. Mathar, Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015.

Crossrefs

Cf. A086241.

Programs

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[3, 2, 2], digits]], 10, digits-1][[1]] (* Vaclav Kotesovec, Jan 22 2021 *)

Extensions

More digits from Vaclav Kotesovec, Jun 27 2020