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Tytuł artykułu

A character-sum estimate and applications

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  • 94 Thornton Road, Bangor, Maine 04401-3336, U.S.A.
Bibliografia
  • [1] N. C. Ankeny, The least quadratic nonresidue, Ann. of Math. 55 (1952), 65-72.
  • [2] E. Bach, Explicit bounds for primality testing and related problems, Math. Comp. 55 (1990), 355-380.
  • [3] E. Bach and L. Huelsbergen, Statistical evidence for small generating sets, Math. Comp. 61 (1993), 69-82.
  • [4] R. Bellman and B. Kotkin, On the numerical solution of a differential-difference equation arising in analytic number theory, Math. Comp. 16 (1962), 473-475.
  • [5] N. G. de Bruijn, The asymptotic behaviour of a function occurring in the theory of primes, J. Indian Math. Soc. (N.S.) 15 (1951), 25-32.
  • [6] A. A. Buchštab [A. A. Bukhshtab], On those numbers in an arithmetic progression all prime factors of which are small in order of magnitude, Dokl. Akad. Nauk SSSR (N.S.) 67 (1949), 5-8 (in Russian).
  • [7] D. A. Burgess, On character sums and L-series, Proc. London Math. Soc. (3) 12 (1962), 193-206.
  • [8] D. A. Burgess, On character sums and L-series. II, Proc. London Math. Soc. 13 (1963), 524-536.
  • [9] D. A. Burgess, A note on the distribution of residues and non-residues, J. London Math. Soc. 38 (1963), 253-256.
  • [10] D. A. Burgess, The character sum estimate with r = 3, J. London Math. Soc. (2) 33 (1986), 219-226.
  • [11] R. J. Burthe, Jr., Upper bounds for least witnesses and generating sets, Acta Arith. 80 (1997), 311-326.
  • [12] J.-M.-F. Chamayou, A probabilistic approach to a differential-difference equation arising in analytic number theory, Math. Comp. 27 (1973), 197-203.
  • [13] H. Davenport and P. Erdős, The distribution of quadratic and higher residues, Publ. Math. Debrecen 2 (1952), 252-265.
  • [14] P. D. T. A. Elliott, Some notes on kth power residues, Acta Arith. 14 (1968), 153-162.
  • [15] P. D. T. A. Elliott, Extrapolating the mean-values of multiplicative functions, Nederl. Akad. Wetensch. Proc. Ser. A 92 (1989), 409-420.
  • [16] P. D. T. A. Elliott, Some remarks about multiplicative functions of modulus ≤ 1, in: Analytic Number Theory (Allerton Park, Ill., 1989), Progr. Math. 85, Birkhäuser Boston, Boston, Mass., 1990, 159-164.
  • [17] E. Fouvry et G. Tenenbaum, Entiers sans grand facteur premier en progressions arithmétiques, Proc. London Math. Soc. (3) 63 (1991), 449-494.
  • [18] S. W. Graham and C. J. Ringrose, Lower bounds for least quadratic nonresidues, in: Analytic Number Theory (Allerton Park, Ill., 1989), Progr. Math. 85, Birkhäuser Boston, Boston, Mass., 1990, 269-309.
  • [19] H. Hasse, Vorlesungen über Zahlentheorie, 2nd ed., Springer, Berlin, 1964.
  • [20] D. G. Hazlewood, Sums over positive integers with few prime factors, J. Number Theory 7 (1975), 189-207.
  • [21] A. Hildebrand and G. Tenenbaum, Integers without large prime factors, J. Théor. Nombres Bordeaux 5 (1993), 411-484.
  • [22] J. H. Jordan, The distribution of cubic and quintic non-residues, Pacific J. Math. 16 (1966), 77-85.
  • [23] J. H. Jordan, The distribution of kth power residues and non-residues, Proc. Amer. Math. Soc. 19 (1968), 678-680.
  • [24] J. H. Jordan, The distribution of kth power non-residues, Duke Math. J. 37 (1970), 333-340.
  • [25] G. Kolesnik and E. G. Straus, On the first occurrence of values of a character, Trans. Amer. Math. Soc. 246 (1978), 385-394.
  • [26] B. V. Levin and A. S. Faĭnleĭb, Application of some integral equations to problems of number theory, Uspekhi Mat. Nauk 22 (1967), no. 3, 119-197 (in Russian); English transl.: Russian Math. Surveys 22 (1967), no. 3, 119-204.
  • [27] J. van de Lune and E. Wattel, On the numerical solution of a differential-difference equation arising in analytic number theory, Math. Comp. 23 (1969), 417-421.
  • [28] H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, Berlin, 1971.
  • [29] K. K. Norton, Upper bounds for kth power coset representatives modulo n, Acta Arith. 15 (1969), 161-179.
  • [30] K. K. Norton, On the distribution of kth power residues and non-residues modulo n, J. Number Theory 1 (1969), 398-418.
  • [31] K. K. Norton, Numbers with small prime factors, and the least kth power non-residue, Mem. Amer. Math. Soc. 106 (1971).
  • [32] K. K. Norton, On the distribution of power residues and non-residues, J. Reine Angew. Math. 254 (1972), 188-203.
  • [33] K. K. Norton, On character sums and power residues, Trans. Amer. Math. Soc. 167 (1972), 203-226.
  • [34] K. K. Norton, Bounds for sequences of consecutive power residues. I, in: Analytic Number Theory, Proc. Sympos. Pure Math. 24, Amer. Math. Soc., Providence, R.I., 1973, 213-220.
  • [35] F. Pappalardi, On minimal sets of generators for primitive roots, Canad. Math. Bull. 38 (1995), 465-468.
  • [36] G. Tenenbaum, Cribler les entiers sans grand facteur premier, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 377-384.
  • [37] T. Z. Xuan, Integers with no large prime factors, Acta Arith. 69 (1995), 303-327.
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