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

Author

Artur Jasinski, Sep 13 2019

Keywords

• nonn
• more

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.

Examples

			   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
		

Links

• 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.

Crossrefs

Cf. A114856, A326890.

Programs

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