A character-sum estimate and applications
Karl K. Norton
Acta Arithmetica, Tome 84 (1998), p. 51-78 / Harvested from The Polish Digital Mathematics Library
Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:207154
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     author = {Karl K. Norton},
     title = {A character-sum estimate and applications},
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     volume = {84},
     year = {1998},
     pages = {51-78},
     zbl = {0914.11049},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav85i1p51bwm}
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Karl K. Norton. A character-sum estimate and applications. Acta Arithmetica, Tome 84 (1998) pp. 51-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav85i1p51bwm/

[000] [1] N. C. Ankeny, The least quadratic nonresidue, Ann. of Math. 55 (1952), 65-72. | Zbl 0046.04006

[001] [2] E. Bach, Explicit bounds for primality testing and related problems, Math. Comp. 55 (1990), 355-380. | Zbl 0701.11075

[002] [3] E. Bach and L. Huelsbergen, Statistical evidence for small generating sets, Math. Comp. 61 (1993), 69-82. | Zbl 0784.11059

[003] [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. | Zbl 0106.10602

[004] [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. | Zbl 0043.06502

[005] [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).

[006] [7] D. A. Burgess, On character sums and L-series, Proc. London Math. Soc. (3) 12 (1962), 193-206. | Zbl 0106.04004

[007] [8] D. A. Burgess, On character sums and L-series. II, Proc. London Math. Soc. 13 (1963), 524-536. | Zbl 0123.04404

[008] [9] D. A. Burgess, A note on the distribution of residues and non-residues, J. London Math. Soc. 38 (1963), 253-256. | Zbl 0118.04703

[009] [10] D. A. Burgess, The character sum estimate with r = 3, J. London Math. Soc. (2) 33 (1986), 219-226. | Zbl 0593.10033

[010] [11] R. J. Burthe, Jr., Upper bounds for least witnesses and generating sets, Acta Arith. 80 (1997), 311-326. | Zbl 0880.11008

[011] [12] J.-M.-F. Chamayou, A probabilistic approach to a differential-difference equation arising in analytic number theory, Math. Comp. 27 (1973), 197-203. | Zbl 0252.65066

[012] [13] H. Davenport and P. Erdős, The distribution of quadratic and higher residues, Publ. Math. Debrecen 2 (1952), 252-265. | Zbl 0050.04302

[013] [14] P. D. T. A. Elliott, Some notes on kth power residues, Acta Arith. 14 (1968), 153-162. | Zbl 0199.36503

[014] [15] P. D. T. A. Elliott, Extrapolating the mean-values of multiplicative functions, Nederl. Akad. Wetensch. Proc. Ser. A 92 (1989), 409-420. | Zbl 0696.10041

[015] [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.

[016] [17] E. Fouvry et G. Tenenbaum, Entiers sans grand facteur premier en progressions arithmétiques, Proc. London Math. Soc. (3) 63 (1991), 449-494. | Zbl 0745.11042

[017] [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.

[018] [19] H. Hasse, Vorlesungen über Zahlentheorie, 2nd ed., Springer, Berlin, 1964.

[019] [20] D. G. Hazlewood, Sums over positive integers with few prime factors, J. Number Theory 7 (1975), 189-207. | Zbl 0302.10037

[020] [21] A. Hildebrand and G. Tenenbaum, Integers without large prime factors, J. Théor. Nombres Bordeaux 5 (1993), 411-484. | Zbl 0797.11070

[021] [22] J. H. Jordan, The distribution of cubic and quintic non-residues, Pacific J. Math. 16 (1966), 77-85. | Zbl 0151.02701

[022] [23] J. H. Jordan, The distribution of kth power residues and non-residues, Proc. Amer. Math. Soc. 19 (1968), 678-680. | Zbl 0164.35102

[023] [24] J. H. Jordan, The distribution of kth power non-residues, Duke Math. J. 37 (1970), 333-340.

[024] [25] G. Kolesnik and E. G. Straus, On the first occurrence of values of a character, Trans. Amer. Math. Soc. 246 (1978), 385-394. | Zbl 0399.10037

[025] [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. | Zbl 0204.06502

[026] [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. | Zbl 0176.46602

[027] [28] H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, Berlin, 1971. | Zbl 0216.03501

[028] [29] K. K. Norton, Upper bounds for kth power coset representatives modulo n, Acta Arith. 15 (1969), 161-179. | Zbl 0177.06801

[029] [30] K. K. Norton, On the distribution of kth power residues and non-residues modulo n, J. Number Theory 1 (1969), 398-418. | Zbl 0185.10503

[030] [31] K. K. Norton, Numbers with small prime factors, and the least kth power non-residue, Mem. Amer. Math. Soc. 106 (1971).

[031] [32] K. K. Norton, On the distribution of power residues and non-residues, J. Reine Angew. Math. 254 (1972), 188-203. | Zbl 0234.10033

[032] [33] K. K. Norton, On character sums and power residues, Trans. Amer. Math. Soc. 167 (1972), 203-226. | Zbl 0238.10023

[033] [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.

[034] [35] F. Pappalardi, On minimal sets of generators for primitive roots, Canad. Math. Bull. 38 (1995), 465-468. | Zbl 0840.11039

[035] [36] G. Tenenbaum, Cribler les entiers sans grand facteur premier, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 377-384.

[036] [37] T. Z. Xuan, Integers with no large prime factors, Acta Arith. 69 (1995), 303-327. | Zbl 0819.11035