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A058303
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Decimal expansion of imaginary part of first nontrivial zero of Riemann zeta function.
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12
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1, 4, 1, 3, 4, 7, 2, 5, 1, 4, 1, 7, 3, 4, 6, 9, 3, 7, 9, 0, 4, 5, 7, 2, 5, 1, 9, 8, 3, 5, 6, 2, 4, 7, 0, 2, 7, 0, 7, 8, 4, 2, 5, 7, 1, 1, 5, 6, 9, 9, 2, 4, 3, 1, 7, 5, 6, 8, 5, 5, 6, 7, 4, 6, 0, 1, 4, 9, 9, 6, 3, 4, 2, 9, 8, 0, 9, 2, 5, 6, 7, 6, 4, 9, 4, 9, 0, 1, 0, 3, 9, 3, 1, 7, 1, 5, 6, 1, 0, 1, 2, 7, 7, 9, 2
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OFFSET
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2,2
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COMMENTS
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"The Riemann Hypothesis, considered by many to be the most important unsolved problem of mathematics, is the assertion that all of zeta's nontrivial zeros line up with the first two all of which lie on the line 1/2 + sqrt(-1)*t, which is called the critical line. It is known that the hypothesis is obeyed for the first billion and a half zeros." (Wagon)
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REFERENCES
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S. Wagon, "Mathematica In Action," W.H. Freeman and Company, NY, 1991, page 361.
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LINKS
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Table of n, a(n) for n=2..106.
Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros
Eric Weisstein's World of Mathematics, Xi-Function
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.
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FORMULA
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Zeta(1/2 + i*14.1347251417346937904572519836...) = 0
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EXAMPLE
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14.1347251417346937904572519835624702707842571156992...
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MATHEMATICA
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FindRoot[ Zeta[1/2 + I*t], {t, 14 + {-.3, +.3}}, AccuracyGoal -> 100, WorkingPrecision -> 120]
RealDigits[N[Im[ZetaZero[1]], 100]][[1]] (* Charles R Greathouse IV, Apr 09 2012 *)
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PROG
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(PARI) solve(x=14, 15, imag(zeta(1/2+x*I)))
\\ Charles R Greathouse IV, Feb 26 2012
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CROSSREFS
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Cf. A013629, A057641, A057640, A058209, A058210.
Sequence in context: A084118 A046071 A078147 * A090724 A134224 A121441
Adjacent sequences: A058300 A058301 A058302 * A058304 A058305 A058306
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KEYWORD
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nonn,cons,easy
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AUTHOR
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Robert G. Wilson v, Dec 08 2000
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STATUS
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approved
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