On the zeros of the Riemann zeta function in the critical strip. II-Reference-Cited by-同舟云学术

On the zeros of the Riemann zeta function in the critical strip. II

Published:1982 Issue:160 Volume:39 Page:681-688
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Brent R. P.,van de Lune J.,te Riele H. J. J.,Winter D. T.

Abstract

We describe extensive computations which show that Riemann’s zeta function ζ ( s ) \zeta (s) has exactly 200,000,001 zeros of the form σ + \sigma + in the region 0 > t > 81 , 702 , 130.19 0 > t > 81,702,130.19 ; all these zeros are simple and lie on the line σ = 1 2 \sigma = \frac {1}{2} . (This extends a similar result for the first 81,000,001 zeros, established by Brent in Math. Comp., v. 33, 1979, pp. 1361-1372.) Counts of the numbers of Gram blocks of various types and the failures of "Rosser’s rule" are given.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1982-39-160/S0025-5718-1982-0669660-1/S0025-5718-1982-0669660-1.pdf

Reference16 articles.

1. R. Backlund, "Sur les zéros de la fonction 𝜁(𝑠) de Riemann," C. R. Acad. Sci. Paris, v. 158, 1914, pp. 1979-1982.

2. On the zeros of the Riemann zeta function in the critical strip;Brent, Richard P.;Math. Comp.,1979

3. R. P. Brent & L. Schoenfeld, Numerical Approximation of the Riemann Zeta Function, Technical Report, Dept. of Computer Science, The Australian National University. (To appear.)

4. Pure and Applied Mathematics, Vol. 58;Edwards, H. M.,1974

5. W. Gabcke, Neue Herleitung und explizite Restabschätzung der Riemann-Siegel-Formel, Dissertation, Universität Göttingen, 1979.

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