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Search: id:A058303
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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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+0
9
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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
(list; cons; graph; listen)
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OFFSET
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2,2
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COMMENT
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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 1.5 * 10^9 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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Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros
Eric Weisstein's World of Mathematics, Xi-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]
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CROSSREFS
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Cf. A013629, A057641, A057640, A058209, A058210.
Sequence in context: A084118 A046071 A078147 this_sequence A090724 A134224 A121441
Adjacent sequences: A058300 A058301 A058302 this_sequence 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 (rgwv(AT)rgwv.com), Dec 08 2000
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