A306339 Decimal expansion of lambda(6) in Li's criterion.

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

Offset: 0

Author

Eric W. Weisstein, Feb 08 2019

Keywords

• nonn
• cons

Examples

			0.8275660122823792974...
		

Links

• E. Bombieri and J. C. Lagarias, Complements to Li's Criterion for the Riemann Hypothesis, J. Number Th. 77(2) (1999), 274-287.
• M. W. Coffey, Relations and positivity results for derivatives of the Riemann xi function, J. Comput. Appl. Math. 166(2) (2004), 525-534.
• Xian-Jin Li, The positivity of a sequence of numbers and the Riemann hypothesis, J. Number Th. 65(2) (1997), 325-333.
• Eric Weisstein's World of Mathematics, Li's Criterion.
• Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros.
• Wikipedia, Li's criterion.

Crossrefs

Cf. A074760 (lambda_1), A104539 (lambda_2), A104540 (lambda_3), A104541 (lambda_4).

Cf. A104542 (lambda_5), A306340 (lambda_7), A306341 (lambda_8).

Programs

Mathematica

RealDigits[With[{e = EulerGamma, g = StieltjesGamma}, 1 + 3 e - 15 e^2 + 20 e^3 - 15 e^4 + 6 e^5 - e^6 + 15 Pi^2/8 + 5 Pi^4/32 + Pi^6/960 - 30 g[1] + 60 e g[1] - 60 e^2 g[1] + 30 e^3 g[1] - 6 e^4 g[1] - 30 g[1]^2 + 30 e g[1]^2 - 9 e^2 g[1]^2 - 2 g[1]^3 + 30 g[2] - 30 e g[2] + 15 e^2 g[2] - 3 e^3 g[2] + 15 g[1] g[2] - 6 e g[1] g[2] - 3 g[2]^2/4 - 10 g[3] + 5 e g[3] - e^2 g[3] - g[1] g[3] + 5 g[4]/4 - e g[4]/4 - g[5]/20 - 3 Log[4 Pi] - 35 Zeta[3]/2 - 93 Zeta[5]/16], 10, 110][[1]]