On smooth integers in short intervals under the Riemann Hypothesis

• Autorzy: Ti Zuo Xuan
• Języki publikacji: EN

Kategorie tematyczne

• 11N25: Distribution of integers with specified multiplicative constraints

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 88
• Numer: 4
• Strony: 327-332

Daty

wydano

1999

otrzymano

1997-04-28

poprawiono

1997-12-22

Twórcy

autor

Ti Zuo Xuan

• Department of Mathematics, Beijing Normal University, Beijing 100875, People's Republic of China

Bibliografia

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