A192492 Decimal expansion of imaginary part of 5th nontrivial zero of Riemann zeta function.
3, 2, 9, 3, 5, 0, 6, 1, 5, 8, 7, 7, 3, 9, 1, 8, 9, 6, 9, 0, 6, 6, 2, 3, 6, 8, 9, 6, 4, 0, 7, 4, 9, 0, 3, 4, 8, 8, 8, 1, 2, 7, 1, 5, 6, 0, 3, 5, 1, 7, 0, 3, 9, 0, 0, 9, 2, 8, 0, 0, 0, 3, 4, 4, 0, 7, 8, 4, 8, 1, 5, 6, 0, 8, 6, 3, 0, 5, 5, 1, 0, 0, 5, 9, 3, 8, 8, 4, 8, 4, 9, 6, 1, 3, 5, 3
Offset: 2
Examples
The zero is at 1/2 + i * 32.9350615877391896906623689640749...
Links
- 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
Crossrefs
Cf. A002410: nearest integer to imaginary part of n-th zero of Riemann zeta function (main entry); also A013629 (floor) and A092783 (ceiling).
The imaginary parts of the first 4 zeros are 14.134725... (A058303), 21.0220396... (A065434), 25.01085758... (A065452), 30.424876... (A065453). Others are A305741 (k=6), A305742 (k=7), A305743 (k=8), A305744 (k=9), A306004 (k=10).
The real parts of the trivial zeros are given by A005843 multiplied by -1 (and ignoring the initial 0 of that sequence).
Programs
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Mathematica
(* ZetaZero was introduced in Version 6.0 *) RealDigits[ZetaZero[5], 10, 100][[1]]
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PARI
solve(y=32,33,real(zeta(1/2+y*I))) \\ Charles R Greathouse IV, Mar 10 2016
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PARI
lfunzeros(lzeta,[32,33])[1] \\ Charles R Greathouse IV, Mar 10 2016
Extensions
Example and cross-references edited by M. F. Hasler, Nov 23 2018
Comments