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A326890
Successive positive minima of Gram's points g(n) of the Riemann zeta function.
6
1, 3, 8, 12, 26, 33, 62, 899, 1288, 3382, 3803, 17161, 97280, 208678, 368382, 45898152, 55785549, 65463721
OFFSET
1,2
COMMENTS
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 negative minima of Gram's points g(n) of the Riemann zeta function see A326891.
a(16)-a(18) follow Korolev 2014.
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. In English.
EXAMPLE
n | a(n) | g(a(n)) = Zeta value
---+--------+---------------------
1 | 1 | 1.457427047874012250
2 | 3 | 0.925264643315366642
3 | 8 | 0.688292371691853238
4 | 12 | 0.538585793754601351
5 | 26 | 0.491521463374527648
6 | 33 | 0.14158237349601719
7 | 62 | 0.00818833702586957
8 | 899 | 0.00443821005886578
9 | 1288 | 0.003877434204568
10 | 3382 | 0.000203064538534
11 | 3803 | 0.000137683252272
12 | 17161 | 0.00011012022914
13 | 97280 | 0.0000123785958
14 | 208678 | 0.000010257478
15 | 368382 | 0.0000000890976
MATHEMATICA
ff = 10; aa = {}; Do[ kk = Re[Zeta[1/2 + I N[ InverseFunction[ RiemannSiegelTheta][n Pi], 10]]]; If[(kk > 0) && (kk < ff), AppendTo[aa, n]; ff = kk], {n, 1, 450000}]; aa
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Artur Jasinski, Sep 13 2019
STATUS
approved