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

%I A326890 #38 Apr 16 2022 15:03:39
%S A326890 1,3,8,12,26,33,62,899,1288,3382,3803,17161,97280,208678,368382,
%T A326890 45898152,55785549,65463721
%N A326890 Successive positive minima of Gram's points g(n) of the Riemann zeta function.
%C A326890 Gram's points occur when the imaginary part of Riemann zeta function is zero but the real part isn't zero.
%C A326890 For very small values of Gram's points the distance between nearest zero of Riemann zeta function is very small.
%C A326890 For successive negative minima of Gram's points g(n) of the Riemann zeta function see A326891.
%C A326890 a(16)-a(18) follow Korolev 2014.
%H A326890 M. A. Korolev, <a href="https://doi.org/10.4213/sm8253">On small values of the Riemann zeta-function at Gram points</a>, Mat. Sb., 2014, Volume 205, Number 1, 67-86. In Russian. <a href="https://doi.org/10.1070/SM2014v205n01ABEH004367">In English</a>.
%e A326890    n |  a(n)  | g(a(n)) = Zeta value
%e A326890   ---+--------+---------------------
%e A326890    1 |      1 | 1.457427047874012250
%e A326890    2 |      3 | 0.925264643315366642
%e A326890    3 |      8 | 0.688292371691853238
%e A326890    4 |     12 | 0.538585793754601351
%e A326890    5 |     26 | 0.491521463374527648
%e A326890    6 |     33 | 0.14158237349601719
%e A326890    7 |     62 | 0.00818833702586957
%e A326890    8 |    899 | 0.00443821005886578
%e A326890    9 |   1288 | 0.003877434204568
%e A326890   10 |   3382 | 0.000203064538534
%e A326890   11 |   3803 | 0.000137683252272
%e A326890   12 |  17161 | 0.00011012022914
%e A326890   13 |  97280 | 0.0000123785958
%e A326890   14 | 208678 | 0.000010257478
%e A326890   15 | 368382 | 0.0000000890976
%t A326890 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
%Y A326890 Cf. A114856, A254297, A255739, A255742, A326502.
%K A326890 nonn,more
%O A326890 1,2
%A A326890 _Artur Jasinski_, Sep 13 2019