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

Author

R. J. Mathar, Aug 01 2010

Keywords

• cons
• nonn

Comments

The absolute value of S(1,chi_3) = sum_{primes p = A000040} A080891(p)/p = -1/2 -1/3 -1/7 +1/11 -1/13 -1/17 -1/23 +...

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.

Crossrefs

Cf. A086241 (mod 3), A086239 (mod 4), A175643 (mod 6).

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[5, 3, 1], digits]], 10, digits-1][[1]] (* Vaclav Kotesovec, Jan 22 2021 *)

Extensions

More digits from Vaclav Kotesovec, Jan 22 2021