On arithmetic progressions having only few different prime factors in comparison with their length

Pieter Moree

Acta Arithmetica (1995)

  • Volume: 70, Issue: 4, page 295-312
  • ISSN: 0065-1036

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Pieter Moree. "On arithmetic progressions having only few different prime factors in comparison with their length." Acta Arithmetica 70.4 (1995): 295-312. <http://eudml.org/doc/206753>.

@article{PieterMoree1995,
author = {Pieter Moree},
journal = {Acta Arithmetica},
keywords = {primes; arithmetic functions; diophantine inequality; conjecture of Shorey and Tijdeman; arithmetic progressions},
language = {eng},
number = {4},
pages = {295-312},
title = {On arithmetic progressions having only few different prime factors in comparison with their length},
url = {http://eudml.org/doc/206753},
volume = {70},
year = {1995},
}

TY - JOUR
AU - Pieter Moree
TI - On arithmetic progressions having only few different prime factors in comparison with their length
JO - Acta Arithmetica
PY - 1995
VL - 70
IS - 4
SP - 295
EP - 312
LA - eng
KW - primes; arithmetic functions; diophantine inequality; conjecture of Shorey and Tijdeman; arithmetic progressions
UR - http://eudml.org/doc/206753
ER -

References

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  1. [E] P. Erdős, Über die Primzahlen gewisser arithmetischer Reihen, Math. Z. 39 (1934), 473-491. Zbl61.0135.03
  2. [G] A. Granville, Integers, without large prime factors, in arithmetic progressions, I, Acta Math. 170 (1993), 255-273. Zbl0784.11045
  3. [Mc1] K. S. McCurley, Explicit estimates for θ(x;3,1) and ψ(x;3,1), Math. Comp. 42 (1984), 287-296. 
  4. [Mc2] K. S. McCurley, Explicit estimates for the error term in the prime number theorem for arithmetic progressions, Math. Comp., 265-285. Zbl0535.10043
  5. [Mo1] P. Moree, Bertrand's Postulate for primes in arithmetical progressions, Comput. Math. Appl. 26 (1993), 35-43. Zbl0789.11001
  6. [Mo2] P. Moree, Psixyology and diophantine equations, Ph.D. thesis, Leiden University, 1993. Zbl0784.11046
  7. [RRu] O. Ramaré and R. Rumely, Primes in arithmetic progressions, Math. Comp., to appear. Zbl0856.11042
  8. [Ri] P. Ribenboim, The Book of Prime Number Records, Springer, New York, 1989 (2nd ed., 1990). 
  9. [RS1] J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94. Zbl0122.05001
  10. [RS2] J. B. Rosser and L. Schoenfeld, Sharper bounds for Chebyshev functions θ(x) and ψ(x), Math. Comp. 29 (1975), 243-269. Zbl0295.10036
  11. [Ru] R. Rumely, Numerical computations concerning the ERH, Math. Comp. 62 (1993), 415-440. Zbl0792.11034
  12. [ST1] T. N. Shorey and R. Tijdeman, On the number of prime factors of an arithmetical progression, Sichuan Daxue Xuebao 26 (1989), 72-74. Zbl0705.11052
  13. [ST2] T. N. Shorey and R. Tijdeman, On the number of prime factors of a finite arithmetical progression, Acta Arith. 61 (1992), 375-390. Zbl0773.11011
  14. [ST3] T. N. Shorey and R. Tijdeman, On the product of terms of a finite arithmetic progression, in: Proc. Conf. Diophantine Approximations and Transcendence Theory, Y.-N. Nakai (ed.), RIMS Kokyuroku 708, Kyoto, 1990, 51-62. 
  15. [ST4] T. N. Shorey and R. Tijdeman, On the greatest prime factor of an arithmetical progression III, in: Proc. Conf. Luminy Transcendence Theory, 1990, Ph. Philippon (ed.), de Gruyter, Berlin, 1992. Zbl0709.11004

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