On smooth integers in short intervals under the Riemann Hypothesis
Ti Zuo Xuan
Acta Arithmetica, Tome 89 (1999), p. 327-332 / Harvested from The Polish Digital Mathematics Library
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Publié le : 1999-01-01
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     title = {On smooth integers in short intervals under the Riemann Hypothesis},
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     volume = {89},
     year = {1999},
     pages = {327-332},
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     language = {en},
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Ti Zuo Xuan. On smooth integers in short intervals under the Riemann Hypothesis. Acta Arithmetica, Tome 89 (1999) pp. 327-332. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav88i4p327bwm/

[000] [1] A. Balog, On the distribution of integers having no large prime factors, Astérisque 147-148 (1987), 27-31. | Zbl 0617.10031

[001] [2] A. Balog and A. Sárközy, On sums of integers having small prime factors: II, Studia Sci. Math. Hungar. 19 (1984), 81-88. | Zbl 0569.10026

[002] [3] J. B. Friedlander and A. Granville, Smoothing 'smooth' numbers, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 339-347. | Zbl 0795.11041

[003] [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. | Zbl 0606.10033

[004] [5] A. Granville, Integers, without large prime factors, in arithmetic progressions. II, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 349-362. | Zbl 0792.11036

[005] [6] G. Harman, Short intervals containing numbers without large prime factors, Math. Proc. Cambridge Philos. Soc. 109 (1991), 1-5. | Zbl 0724.11041

[006] [7] A. Hildebrand, On the number of positive integers ≤x and free of prime factors >y, J. Number Theory 22 (1986), 289-307. | Zbl 0575.10038

[007] [8] A. Hildebrand and G. Tenenbaum, On integers free of large prime factors, Trans. Amer. Math. Soc. 296 (1986), 265-290. | Zbl 0601.10028

[008] [9] A. Hildebrand and G. Tenenbaum, Integers without large prime factors, J. Théor. Nombres Bordeaux 5 (1993), 411-484. | Zbl 0797.11070

[009] [10] H. L. Montgomery, Topics in Multiplicative Number Theory, Springer, 1971. | Zbl 0216.03501

[010] [11] H. E. Richert, Zur Abschätzung der Riemannschen Zetafunktion in der Nähe der Vertikalen σ=1, Math. Ann. 169 (1967), 97-101. | Zbl 0161.04802

[011] [12] E. C. Titchmarsh, The Theory of the Riemann Zeta Function, 2nd ed., revised by D. R. Heath-Brown, Oxford Univ. Press, 1986. | Zbl 0601.10026