

A058303


Decimal expansion of imaginary part of first nontrivial zero of Riemann zeta function.


15



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

2,2


COMMENTS

"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)


REFERENCES

P. J. Forrester, A. Mays, Finite size corrections in random matrix theory and Odlyzko's data set for the Riemann zeros, arXiv preprint arXiv:1506.06531, 2015
S. Wagon, "Mathematica In Action," W.H. Freeman and Company, NY, 1991, page 361.


LINKS

Table of n, a(n) for n=2..106.
Fredrik Johansson, The first nontrivial zero to over 300000 decimal digits
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
Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros
Eric Weisstein's World of Mathematics, XiFunction
Index entries for zeta function.


FORMULA

Zeta(1/2 + i*14.1347251417346937904572519836...) = 0


EXAMPLE

14.1347251417346937904572519835624702707842571156992...


MATHEMATICA

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 *)


PROG

(PARI) solve(x=14, 15, imag(zeta(1/2+x*I)))
\\ Charles R Greathouse IV, Feb 26 2012


CROSSREFS

Cf. A013629, A057641, A057640, A058209, A058210.
Sequence in context: A084118 A046071 A078147 * A240935 A090724 A134224
Adjacent sequences: A058300 A058301 A058302 * A058304 A058305 A058306


KEYWORD

nonn,cons,easy


AUTHOR

Robert G. Wilson v, Dec 08 2000


STATUS

approved



