On smooth integers in short intervals under the Riemann Hypothesis

Ti Zuo Xuan

Acta Arithmetica (1999)

  • Volume: 88, Issue: 4, page 327-332
  • ISSN: 0065-1036

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Ti Zuo Xuan. "On smooth integers in short intervals under the Riemann Hypothesis." Acta Arithmetica 88.4 (1999): 327-332. <http://eudml.org/doc/207250>.

@article{TiZuoXuan1999,
author = {Ti Zuo Xuan},
journal = {Acta Arithmetica},
keywords = {short intervals; Riemann hypothesis; integers with restricted prime factors},
language = {eng},
number = {4},
pages = {327-332},
title = {On smooth integers in short intervals under the Riemann Hypothesis},
url = {http://eudml.org/doc/207250},
volume = {88},
year = {1999},
}

TY - JOUR
AU - Ti Zuo Xuan
TI - On smooth integers in short intervals under the Riemann Hypothesis
JO - Acta Arithmetica
PY - 1999
VL - 88
IS - 4
SP - 327
EP - 332
LA - eng
KW - short intervals; Riemann hypothesis; integers with restricted prime factors
UR - http://eudml.org/doc/207250
ER -

References

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  1. [1] A. Balog, On the distribution of integers having no large prime factors, Astérisque 147-148 (1987), 27-31. Zbl0617.10031
  2. [2] A. Balog and A. Sárközy, On sums of integers having small prime factors: II, Studia Sci. Math. Hungar. 19 (1984), 81-88. Zbl0569.10026
  3. [3] J. B. Friedlander and A. Granville, Smoothing 'smooth' numbers, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 339-347. Zbl0795.11041
  4. [4] J. B. Friedlander and J. C. Lagarias, On the distribution in short intervals of integers having no large prime factors, J. Number Theory 25 (1987), 249-273. Zbl0606.10033
  5. [5] A. Granville, Integers, without large prime factors, in arithmetic progressions. II, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 349-362. Zbl0792.11036
  6. [6] G. Harman, Short intervals containing numbers without large prime factors, Math. Proc. Cambridge Philos. Soc. 109 (1991), 1-5. Zbl0724.11041
  7. [7] A. Hildebrand, On the number of positive integers ≤x and free of prime factors >y, J. Number Theory 22 (1986), 289-307. Zbl0575.10038
  8. [8] A. Hildebrand and G. Tenenbaum, On integers free of large prime factors, Trans. Amer. Math. Soc. 296 (1986), 265-290. Zbl0601.10028
  9. [9] A. Hildebrand and G. Tenenbaum, Integers without large prime factors, J. Théor. Nombres Bordeaux 5 (1993), 411-484. Zbl0797.11070
  10. [10] H. L. Montgomery, Topics in Multiplicative Number Theory, Springer, 1971. Zbl0216.03501
  11. [11] H. E. Richert, Zur Abschätzung der Riemannschen Zetafunktion in der Nähe der Vertikalen σ=1, Math. Ann. 169 (1967), 97-101. Zbl0161.04802
  12. [12] E. C. Titchmarsh, The Theory of the Riemann Zeta Function, 2nd ed., revised by D. R. Heath-Brown, Oxford Univ. Press, 1986. Zbl0601.10026

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