On the zeros of the riemann zeta function in the critical strip IV

Mathematics of Computation

Volumn 46, Issue 174, 1986, Pages 667-681

  Van De Lune, J ^a   Te Riele, H J J ^a   Winter, D T ^a  

^a CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966203701     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1986-0829637-3     Document Type: Article

References (14)

1. R. P. Brent, "On the zéros of the Riemann zeta function in the critical strip, " Math. Comp., v. 33, 1979, pp. 1361-1372.
2. R. P. BRENT, J. VAN DE LUNE, H. J. J. TE RIELE & D. T. WINTER, "On the zéros of the Riemann zeta function in the critical Strip. II, " Math. Comp., v. 39, 1982, pp. 681-688.
3. E. KARKOSCHKA & P. WERNER, "Einige Ausnahmen zur Rosserschen Regel in der Theorie der Riemannschen Zetafunktion, " Computing, v. 27, 1981, pp. 57-69.
4. I. KATAI, "On oscillations of number-theoretic functions, " Acta Arith., v. 13, 1967, pp. 107-122.
5. R. S. LEHMAN, "On the différence π(x)- li(x), " Acta Arith., v. 11, 1966, pp. 397-410.
6. J. VAN DE LUNE, H. J. J. TE RIELE & D. T. WINTER, Rigorous High Speed Separation of Zeros of Riemann's Zeta Function, Report NW 113/81, Mathematical Centre, Amsterdam, October, 1981.
7. J. VAN DE LUNE & H. J. J. TE RIELE, "On the zéros of the Riemann zeta function in the critical strip. III, " Math. Comp., v. 41, 1983, pp. 759-767.
8. J. PINTZ, "On the sign changes of M(x) = Σn<=xµ(n), " Analysis, v. 1, 1981, pp. 191-195.
9. H. J. J. TE RIELE, D. T. WINTER & J. VAN DE LUNE, Numerical Vérification of the Riemann Hypothesis on the CYBER 205, in: Proc. International Supercomputer Applications Symp. (A. Emmen, ed.), North-Holland, Amsterdam, 1985, pp. 33-38.
10. J. B. ROSSER & L. SCHOENFELD, "Approximate formulas for fonctions of prime numbers, " Illinois J. Math.y v. 6, 1962, pp. 64-94.
11. J. B. ROSSER & L. SCHOENFELD, "Sharper bounds for the Chebyshev fonctions ø(x) and ψ(x), " Math. Comp., v. 29, 1975, pp. 243-269.
12. L. SCHOENFELD, "Sharper bounds for the Chebyshev fonctions ø (x) and ψ (x). II, " Math. Comp., v. 30, 1976, pp. 337-360.
13. L. SCHOENFELD, "An improved estímate for the summatory function of the Moebius function, " Acta Arith., v. 15, 1969, pp. 221-233.
14. D. T. WINTER & H. J. J. TE RIELE, "Optimization of a program for the vérification of the Riemann hypothesis, " Supercomputer, v. 5, 1985, pp. 29-32.