On Šnirelman's constant under the Riemann hypothesis

Leszek Kaniecki

Acta Arithmetica (1995)

  • Volume: 72, Issue: 4, page 361-374
  • ISSN: 0065-1036

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Leszek Kaniecki. "On Šnirelman's constant under the Riemann hypothesis." Acta Arithmetica 72.4 (1995): 361-374. <http://eudml.org/doc/206802>.

@article{LeszekKaniecki1995,
author = {Leszek Kaniecki},
journal = {Acta Arithmetica},
keywords = {Schnirelman constant; Riemann hypothesis; Goldbach's conjecture; primes in short intervals},
language = {eng},
number = {4},
pages = {361-374},
title = {On Šnirelman's constant under the Riemann hypothesis},
url = {http://eudml.org/doc/206802},
volume = {72},
year = {1995},
}

TY - JOUR
AU - Leszek Kaniecki
TI - On Šnirelman's constant under the Riemann hypothesis
JO - Acta Arithmetica
PY - 1995
VL - 72
IS - 4
SP - 361
EP - 374
LA - eng
KW - Schnirelman constant; Riemann hypothesis; Goldbach's conjecture; primes in short intervals
UR - http://eudml.org/doc/206802
ER -

References

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  1. [1] J. R. Chen and T. Z. Wang, On the odd Goldbach problem, Acta Math. Sinica 32 (1989), 702-718 (in Chinese). Zbl0695.10041
  2. [2] H. Davenport, Multiplicative Number Theory, Springer, 1980. 
  3. [3] M. Deshouillers, Sur la constante de Schnirelmann, Sém. Delange-Pisot-Poitou, 17e année, 1975/6, fasc. 2, exp. No. G 16, 6 p., Paris, 1977. 
  4. [4] H. M. Edwards, Riemann's Zeta Function, Academic Press, 1974. Zbl0315.10035
  5. [5] A. Granville, J. van de Lune and H. J. J. te Riele, Checking the Goldbach conjecture on a vector computer, in: Number Theory and Applications, R. A. Mollin (ed.), Kluwer, Dordrecht, 1989, 423-433. Zbl0679.10002
  6. [6] L. Kaniecki, Some remarks on a result of A. Selberg, Funct. Approx. Comment. Math. 22 (1993), 171-179. Zbl0824.11050
  7. [7] H. L. Montgomery and R. C. Vaughan, The exceptional set in Goldbach's problem, Acta Arith. 27 (1975), 353-370. Zbl0301.10043
  8. [8] K. Prachar, Primzahlverteilung, Springer, 1957. 
  9. [9] O. Ramaré, On Šnirelman's constant, Les prépublication de l'Institut Élie Cartan 95, no 4, to appear. 
  10. [10] H. Riesel and R. C. Vaughan, On sums of primes, Ark. Mat. 21 (1983), 45-74. Zbl0516.10044
  11. [11] L. Schoenfeld, Sharper bounds for the Čebyshev functions ψ and θ, II, Math. Comp. 30 (1976), 337-360. Zbl0326.10037
  12. [12] A. Selberg, On the normal density of primes in small intervals and the differences between consecutive primes, Arch. Math. Naturvid. (6) 47 (1943), 87-105. Zbl0063.06869
  13. [13] M. K. Shen, On checking the Goldbach conjecture, Nordisk Tidskr. 4 (1964), 243-245. Zbl0136.33602
  14. [14] M. K. Sinisalo, Checking the Goldbach conjecture up to 4· 10¹¹, Math. Comp. 61 (1993), 931-934. Zbl0783.11037
  15. [15] M. L. Stein and P. R. Stein, New experimental results on the Goldbach conjecture, Math. Mag. 38 (1965), 72-80. Zbl0132.03102
  16. [16] J. Young and A. Potler, First occurrence prime gaps, Math. Comp. 52 (1989), 221-224. Zbl0661.10011

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