A065434 Decimal expansion of imaginary part of 2nd nontrivial zero of Riemann zeta function.

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

Offset: 2

Author

N. J. A. Sloane, Nov 24 2001

Keywords

• nonn
• cons

Examples

			The zero is at 1/2 + i*21.0220396387715549926284795938969...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.15.3, p. 138.

Links

• Enrico Bombieri, Problems of the Millennium: the Riemann Hypothesis, Clay Mathematics Institute.
• Andrew M. Odlyzko, The first 100 (non trivial) zeros of the Riemann Zeta function, to over 1000 decimal digits each, AT&T Labs - Research.
• Andrew M. Odlyzko, Tables of zeros of the Riemann zeta function
• Index entries for zeta function.

Crossrefs

Imaginary part of k-th nontrivial zero of Riemann zeta function: A058303 (k=1), A065434 (k=2: this), A065452 (k=3), A065453 (k=4), A192492 (k=5), A305741 (k=6), A305742 (k=7), A305743 (k=8), A305744 (k=9), A306004 (k=10).

Cf. A002410 (round), A013629 (floor).

Programs

Maple

Digits:= 150; Re(fsolve(Zeta(1/2+I*t)=0, t=21)); # Iaroslav V. Blagouchine, Jun 25 2016

Mathematica

ZetaZero[2] // Im // RealDigits[#, 10, 99]& // First (* Jean-François Alcover, Mar 05 2013 *)

PARI

solve(x=21,22,real(zeta(1/2+x*I))) \\ Charles R Greathouse IV, Jun 30 2011

PARI

lfunzeros(1,[21,22])[1] \\ M. F. Hasler, Nov 23 2018