A065452 Decimal expansion of imaginary part of 3rd nontrivial zero of Riemann zeta function.

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

Offset: 2

Author

N. J. A. Sloane, Nov 24 2001

Keywords

• nonn
• cons

Comments

See A002410 and A058303 for more information.

Examples

			The zero is at 1/2 + i * 25.01085758014568876321379099256282181865954967...
		

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

• G. C. Greubel, Table of n, a(n) for n = 2..10000
• 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), A065452 (k=3: this), A065453 (k=4), A192492 (k=5), A305741 (k=6), A305742 (k=7), A305743 (k=8), A305744 (k=9), A306004 (k=10).

Cf. A002410 (these values rounded to nearest integer), A013629 (floor), A092783 (ceiling).

Programs

Mathematica

ZetaZero[3] // Im // RealDigits[#, 10, 99]& // First (* Jean-François Alcover, Mar 05 2013 *)

PARI

solve(x=25,25.1,real(zeta(1/2+x*I))) \\ Charles R Greathouse IV, Jun 30 2011

PARI

lfunzeros(1,[25,26])[1] \\ or: lfunzeros(1,26)[3]. - M. F. Hasler, Nov 23 2018

Extensions

Minor edits by M. F. Hasler, Nov 23 2018