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A088749 Numbers of the lines Im zeta(sigma + i t)=0 that escape to the right. 2

%I #18 Mar 11 2023 08:43:28

%S -3,-1,1,3,9,11,17,23,29,35,41,47,53,59,69,75,81,91,97,103,113,123,

%T 129,135,145,155,161,171,181,187,197,207,217,223,237,247,253,263,273,

%U 283,293,307,313,323,329,343,353,359,373,383,393,403,417,423,437,451,457,467,481,491,501,511,525,535,545,559,569

%N Numbers of the lines Im zeta(sigma + i t)=0 that escape to the right.

%C This sequence contains important information about the graphics of the lines Re zeta(s)=0 and Im zeta(s)=0, where zeta(s) is the Riemann zeta function. Only the first two terms are negative. It is an increasing sequence. The values of this sequence alternatively are congruent to 1 or 3 (mod 4).

%D J. van de Lune, Some observations concerning the zero-curves of the Real and imaginary parts of Riemann's zeta function, Afdeling Zuivere Wiskunde [Department of Pure Mathematics], 201. Mathematisch Centrum, Amsterdam, 1983. i+25 pp

%D A. Speiser, Geometrisches zur Riemannschen Zetafunktion, Math. Ann., Vol. 110 (1935), pp. 514-521

%D Albert A. Utzinger, Die reellen Züge der Riemann'schen Zetafunktionen, Zürich Univ. Phil. Dissertation, Leemann, 1934.

%H J. Arias-de-Reyna, <a href="https://arxiv.org/abs/math/0309433">X-Ray of Riemann zeta-function</a>, arXiv:math/0309433 [math.NT] (2003), 42 p.

%e a(4)=3 because the line number 3, that pass for the second nontrivial zero of the zeta function, is the fourth parallel line that goes to infinity to the right of the s-plane.

%Y Cf. A088750.

%K hard,sign

%O 1,1

%A _Juan Arias-de-Reyna_, Oct 14 2003

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Last modified December 7 21:37 EST 2023. Contains 367662 sequences. (Running on oeis4.)