Integers without large prime factors in short intervals and arithmetic progressions

• Autorzy: Glyn Harman
• 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: 91
• Numer: 3
• Strony: 279-289

Daty

wydano

1999

otrzymano

1999-02-19

Twórcy

autor

Glyn Harman

• School of Mathematics, Cardiff University, P.O.Box No. 926, Cardiff CF2 4YH, Wales, U.K.

Bibliografia

• [1] R. C. Baker, The greatest prime factor of the integers in an interval, Acta Arith. 47 (1986), 193-231.
• [2] R. C. Baker and G. Harman, Shifted primes without large prime factors, ibid. 83 (1998), 331-361.
• [3] A. Balog, p+a without large prime factors, Sém. Théorie des Nombres Bordeaux (1983-84), exposé 31.
• [4] A. Balog and C. Pomerance, The distribution of smooth numbers in arithmetic progressions, Proc. Amer. Math. Soc. 115 (1992), 33-43.
• [5] D. A. Burgess, On character sums and L-series, II, Proc. London Math. Soc. (3) 13 (1963), 525-536.
• [6] D. A. Burgess, The character sum estimate with r=3, J. London Math. Soc. (2) 33 (1986), 219-226.
• [7] J. B. Friedlander, Integers free from large and small primes, Proc. London Math. Soc. (3) 33 (1976), 565-576.
• [8] J. B. Friedlander, Shifted primes without large prime factors, in: Number Theory and Applications, 1989, Kluwer, Berlin, 1990, 393-401.
• [9] J. B. Friedlander and A. Granville, Smoothing `smooth' numbers, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 339-347.
• [10] J. B. Friedlander and J. C. Lagarias, On the distribution in short intervals of integers having no large prime factor, J. Number Theory 25 (1987), 249-273.
• [11] S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, London Math. Soc. Lecture Note Ser. 126, Cambridge Univ. Press, 1991.
• [12] A. Granville, Integers, without large prime factors, in arithmetic progressions I, Acta Math. 170 (1993), 255-273.
• [13] A. Granville, Integers, without large prime factors, in arithmetic progressions II, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 349-362.
• [14] G. Harman, Diophantine approximation with square-free integers, Math. Proc. Cambridge Philos. Soc. 95 (1984), 381-388.
• [15] G. Harman, Short intervals containing numbers without large prime factors, ibid. 109 (1991), 1-5.
• [16] H. Iwaniec, Rosser's sieve, Acta Arith. 36 (1980), 171-202.
• [17] H. W. Lenstra, Jr., J. Pila and C. Pomerance, A hyperelliptic smoothness test I, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 397-408.
• [18] H.-Q. Liu and J. Wu, Numbers with a large prime factor, Acta Arith. 89 (1999), 163-187.
• [19] H. L. Montgomery, Topics in Multiplicative Number Theory, Springer, 1971.