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

-3, -1, 1, 3, 9, 11, 17, 23, 29, 35, 41, 47, 53, 59, 69, 75, 81, 91, 97, 103, 113, 123, 129, 135, 145, 155, 161, 171, 181, 187, 197, 207, 217, 223, 237, 247, 253, 263, 273, 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

Offset

1,1

Comments

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).

References

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

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

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

Links

Table of n, a(n) for n=1..67.

J. Arias-de-Reyna, X-Ray of Riemann zeta-function, arXiv:math/0309433 [math.NT] (2003), 42 p.

Example

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.

Crossrefs

Cf. A088750.

Sequence in context: A199922 A112508 A260883 * A024737 A024958 A014516

Adjacent sequences: A088746 A088747 A088748 * A088750 A088751 A088752

Keyword

hard,sign

Author

Juan Arias-de-Reyna, Oct 14 2003

Status

approved