A326891 Successive negative minima of Gram's points g(n) of the Riemann zeta function.

126, 134, 777, 1165, 2808, 3782, 12174, 14374, 23149, 60780, 117807, 126085

Offset

1,1

Comments

This sequence is subset of A114856.

Gram's points occur when the imaginary part of Riemann zeta function is zero but the real part isn't zero.

For very small values of Gram's points, the distance between nearest zero of Riemann zeta function is very small.

For successive positive minima of Gram's points g(n) of the Riemann zeta function see A326890.

Links

Table of n, a(n) for n=1..12.

M. A. Korolev, On small values of the Riemann zeta-function at Gram points, Mat. Sb., 2014, Volume 205, Number 1, 67-86. In Russian.

Example

   n |  a(n)  | g(a(n)) = Zeta value
  ---+--------+---------------------
   1 |    126 | -0.02762949885719994
   2 |    134 | -0.01690039090339079
   3 |    777 | -0.00964626429746985
   4 |   1165 | -0.008575843736423
   5 |   2808 | -0.005747300941326
   6 |   3782 | -0.000760294730822
   7 |  12174 | -0.00045763304501
   8 |  14374 | -0.00027891005688
   9 |  23149 | -0.00007068683846
  10 |  60780 | -0.0000398945276
  11 | 117807 | -0.0000229487717
  12 | 126085 | -0.0000077126884

Mathematica

ee = 10; cc = {}; Do[kk = Re[Zeta[1/2 + I N[InverseFunction[ RiemannSiegelTheta][n Pi], 10]]]; If[(kk < 0) && (Abs[kk] < ee), AppendTo[cc, n]; ee = Abs[kk]], {n, 1, 1000000}]; aa

Crossrefs

Cf. A114856, A326890.

Sequence in context: A045167 A216063 A114856 * A165019 A025388 A025389

Adjacent sequences: A326888 A326889 A326890 * A326892 A326893 A326894

Keyword

nonn,more

Author

Artur Jasinski, Sep 13 2019

Status

approved