ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

  1. Department of Mathematics, Princeton University, Fine Hall - Washington Road, Princeton, New Jersey 08544-1000, U.S.A.

Bibliography

  1. [E] P. Erdős, Über die Primzahlen gewisser arithmetischer Reihen, Math. Z. 39 (1934), 473-491.
  2. [G] A. Granville, Integers, without large prime factors, in arithmetic progressions, I, Acta Math. 170 (1993), 255-273.
  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.
  5. [Mo1] P. Moree, Bertrand's Postulate for primes in arithmetical progressions, Comput. Math. Appl. 26 (1993), 35-43.
  6. [Mo2] P. Moree, Psixyology and diophantine equations, Ph.D. thesis, Leiden University, 1993.
  7. [RRu] O. Ramaré and R. Rumely, Primes in arithmetic progressions, Math. Comp., to appear.
  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.
  10. [RS2] J. B. Rosser and L. Schoenfeld, Sharper bounds for Chebyshev functions θ(x) and ψ(x), Math. Comp. 29 (1975), 243-269.
  11. [Ru] R. Rumely, Numerical computations concerning the ERH, Math. Comp. 62 (1993), 415-440.
  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.
  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.
  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.
Pages:
295-312
Main language of publication
English
Received
1991-10-08
Accepted
1994-11-07
Published
1995
Exact and natural sciences