On the fluctuations of littlewood for primes of the form An 1

Mathematics of Computation

Volumn 32, Issue 141, 1978, Pages 281-286

  Bays, Carter ^a   Hudson, Richard H ^a  

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966203307     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1978-0476615-8     Document Type: Article

References (17)

1. RICHARD P. BRENT, Tables Conceming Irregularities in the Distribution of Primes and Twin Primes to 101, Computer Centre, Australian National University, Canberra, Australia 1975.
2. P. L. CHEBYSHEV, “Lettre de M. le professeur Tche'bychev á M. Fuss sur un nouveaux théorème relatif aux nombres premiers contenus dans les formes 4n ± 1 et 4n ± 3,” Bull, de la Classe Phys. de VAcad. Imp. des Sciences, St. Petersburg, v. 11, 1853, p. 208.
3. G. H. HARDY & J. E. LITTLEWOOD, “Contributions to the theory of the Riemann-zeta function and the theory of the distribution of primes,” Acta Math., J. 41, 1917, pp. 119—196.
4. RICHARD H. HUDSON & ALFRED BRAUER, “On the exact number of primes in the arithmetic progressions 4n ± 1 and 6n ± 1,” J. Reine Angew. Math., v. 281, 1976, pp. 23-29.
5. RICHARD H. HUDSON & CARTER BAYS, “The mean behavior of primes in arithmetic progressions,” J. Reine Angew. Math., v. 295, 1977.
6. A. E. INGHAM, The Distribution of Prime Numbers, Stechert-Hafner, New York, 1964.
7. S. KNAPOWSKI & P. TURÁN, “Comparative prime-number theory. III. Continuation of the study of comparison of the progressions = 1 (mod k) and =1 (mod fc),” Acta Math. Acad. Sci. Hungar., v. 13, 1962, pp. 343-364.
8. S. KNAPOWSKI & P. TURÀN, “Comparative prime-number theory. VII. The problem of sign-changes in the general case,” Acta Math. Acad. Sci. Hungar., v. 14, 1963, pp. 241-250.
9. S. KNAPOWSKI & P. TURÁN, “Further developments in the comparative prime-num: Ber theory. I,” Acta Arith., v. 9, 1964, pp. 23-40.
10. S. KNAPOWSKI & P. TURÁN, “Further developments in the comparative prime-num-ber theory. II, A modification of Chebyshev’s assertion,” Acta Arith., v. 10, 1964, pp. 293-313.
11. E. LANDAU, Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea, New York, 1953.
12. E. LANDAU, “Über einige Ältere Vermutungen und Behauptungen in der Primzahl-theorie,” Math Z., v. 1, 1919, pp. 1-24.
13. JOHN LEECH, “Note on the distribution of prime numbers,”J. London Math. Soc., v. 32, 1957, pp. 56-58.
14. D. H. LEHMER, Personal communication to Richard Hudson from Daniel Shanks (May 24, 1976).
15. J. E. LITTLEWOOD, “Sur la distribution des nombres premiers,” Comptes Rendus, v. 158, 1914, pp. 1869-1872.
16. G. PÓLYA, “On polar singularities of power series and of Dirichlet series,” Proc. London Math. Soc. (2), v. 33, 1932, pp. 85-101.
17. DANIEL SHANKS, “Quadratic residues and the distribution of primes,” Math. Comp., v. 13, 1959, pp. 272-284.