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
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
KEYWORD
hard,sign
AUTHOR
Juan Arias-de-Reyna, Oct 14 2003
STATUS
approved