Numbers with a large prime factor
Hong-Quan Liu ; Jie Wu
Acta Arithmetica, Tome 89 (1999), p. 163-187 / Harvested from The Polish Digital Mathematics Library
Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:207262
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     author = {Hong-Quan Liu and Jie Wu},
     title = {Numbers with a large prime factor},
     journal = {Acta Arithmetica},
     volume = {89},
     year = {1999},
     pages = {163-187},
     zbl = {0937.11038},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav89i2p163bwm}
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Hong-Quan Liu; Jie Wu. Numbers with a large prime factor. Acta Arithmetica, Tome 89 (1999) pp. 163-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav89i2p163bwm/

[000] [1] R. C. Baker, The greatest prime factor of the integers in an interval, Acta Arith. 47 (1986), 193-231. | Zbl 0553.10035

[001] [2] R. C. Baker and G. Harman, Numbers with a large prime factor, Acta Arith. 73 (1995), 119-145.

[002] [3] R. C. Baker, G. Harman and J. Rivat, Primes of the form [nc], J. Number Theory 50 (1995), 261-277. | Zbl 0822.11062

[003] [4] A. Balog, Numbers with a large prime factor I, Studia Sci. Math. Hungar. 15 (1980), 139-146; II, in: Topics in Classical Number Theory, Colloq. Math. Soc. János Bolyai 34, North-Holland, 1984, 49-67. | Zbl 0445.10033

[004] [5] A. Balog, G. Harman and J. Pintz, Numbers with a large prime factor IV, J. London Math. Soc. (2) 28 (1983), 218-226. | Zbl 0514.10034

[005] [6] E. Fouvry, Sur le théorème de Brun-Titchmarsh, Acta Arith. 43 (1984), 417-424.

[006] [7] E. Fouvry and H. Iwaniec, Exponential sums with monomials, J. Number Theory 33 (1989), 311-333. | Zbl 0687.10028

[007] [8] S. W. Graham, The greatest prime factor of the integers in an interval, J. London Math. Soc. (2) 24 (1981), 427-440. | Zbl 0442.10028

[008] [9] S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, Cambridge Univ. Press, 1991. | Zbl 0713.11001

[009] [10] G. Harman, On the distribution of αp modulo one, J. London Math. Soc. (2) 27 (1983), 9-13. | Zbl 0504.10018

[010] [11] D. R. Heath-Brown, The Pjateckiĭ-Šapiro prime number theorem, J. Number Theory 16 (1983), 242-266. | Zbl 0513.10042

[011] [12] D. R. Heath-Brown, The largest prime factor of the integers in an interval, Sci. China Ser. A 39 (1996), 449-476. | Zbl 0867.11064

[012] [13] D. R. Heath-Brown and C. H. Jia, The largest prime factor of the integers in an interval II, J. Reine Angew. Math. 498 (1998), 35-59. | Zbl 1066.11506

[013] [14] M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford Sci. Publ., Clarendon Press, Oxford, 1996.

[014] [15] H. Iwaniec, A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320. | Zbl 0444.10038

[015] [16] C. H. Jia, The greatest prime factor of the integers in an interval I, Acta Math. Sinica 29 (1986), 815-825; II, Acta Math. Sinica 32 (1989), 188-199; III, Acta Math. Sinica (N.S.) 9 (1993), 321-336; IV, Acta Math. Sinica 12 (1996), 433-445. | Zbl 0621.10025

[016] [17] M. Jutila, On numbers with a large prime factor IV, J. Indian Math. Soc. (N.S.) 37 (1973), 43-53.

[017] [18] H.-Q. Liu, The greatest prime factor of the integers in an interval, Acta Arith. 65 (1993), 301-328. | Zbl 0797.11071

[018] [19] H.-Q. Liu, A special triple exponential sum, Mathematika 42 (1995), 137-143. | Zbl 0829.11042

[019] [20] K. Ramachandra, A note on numbers with a large prime factor I, J. London Math. Soc. (2) 1 (1969), 303-306; II, J. Indian Math. Soc. 34 (1970), 39-48. | Zbl 0179.07301

[020] [21] E. C. Titchmarsh, The Theory of the Riemann Zeta-function, 2nd ed., revised by D. R. Heath-Brown, Clarendon Press, Oxford, 1986. | Zbl 0601.10026

[021] [22] J. Wu, Nombres 𝓑-libres dans les petits intervalles, Acta Arith. 65 (1993), 97-116.