login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; constant; graph; refs; listen; history; text; internal format)
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

S. Wagon, "Mathematica In Action," W.H. Freeman and Company, NY, 1991, page 361.

LINKS

Table of n, a(n) for n=2..106.

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 [math-ph], 2015.

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, Xi-Function

Index entries for zeta function.

FORMULA

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

EXAMPLE

14.1347251417346937904572519835624702707842571156992...

MAPLE

Digits:= 150; Re(fsolve(Zeta(1/2+I*t)=0, t=14.13)); # Iaroslav V. Blagouchine, Jun 24 2016

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 4 17:40 EST 2016. Contains 278755 sequences.