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
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
KEYWORD
nonn,more
AUTHOR
Artur Jasinski, Sep 13 2019
STATUS
approved