@article{bwmeta1.element.bwnjournal-article-aav91i3p249bwm,
author = {Todd Cochrane and Zhiyong Zheng},
title = {Pure and mixed exponential sums},
journal = {Acta Arithmetica},
volume = {89},
year = {1999},
pages = {249-278},
zbl = {0937.11031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav91i3p249bwm}
}
Todd Cochrane; Zhiyong Zheng. Pure and mixed exponential sums. Acta Arithmetica, Tome 89 (1999) pp. 249-278. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav91i3p249bwm/
[000] [1] E. Bombieri, On exponential sums in finite fields, Amer. J. Math. 88 (1966), 71-105. | Zbl 0171.41504
[001] [2] J. H. H. Chalk, On Hua's estimate for exponential sums, Mathematika 34 (1987), 115-123. | Zbl 0621.10024
[002] [3] J. R. Chen, On Professor Hua's estimate of exponential sums, Sci. Sinica 20 (1977), 711-719. | Zbl 0374.10024
[003] [4] T. Cochrane and Z. Y. Zheng, Exponential sums with rational function entries, to appear.
[004] [5] P. Ding, An improvement to Chalk's estimation of exponential sums, Acta Arith. 59 (1991), 149-155. | Zbl 0697.10031
[005] [6] P. Ding, On a conjecture of Chalk, J. Number Theory 65 (1997), 116-129. | Zbl 0876.11044
[006] [7] G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio Numerorum' 1: A new solution of Waring's problem, Nachr. K. Gesellschaft Wiss. Göttingen Math.-Phys. Kl. 1929, 33-54. | Zbl 47.0114.02
[007] [8] G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio Numerorum', Math. Z. 23 (1925), 1-37. | Zbl 51.0148.01
[008] [9] D. R. Heath-Brown, An estimate on Heilbronn's exponential sum, in: Analytic Number Theory, Vol. 2 (Allerton Park, IL, 1995), Progr. Math. 139, Birkhäuser, Boston, 1996, 451-463. | Zbl 0857.11041
[009] [10] L. K. Hua, On exponential sums, J. Chinese Math. Soc. 20 (1940), 301-312. | Zbl 0061.06608
[010] [11] L. K. Hua, On exponential sums, Sci. Record (Peking) (N.S.) 1 (1957), 1-4. | Zbl 0083.04204
[011] [12] L. K. Hua, Additive Primzahltheorie, Teubner, Leipzig, 1959, 2-7.
[012] [13] W. K. A. Loh, Hua's Lemma, Bull. Austral. Math. Soc. (3) 50 (1994), 451-458. | Zbl 0833.11040
[013] [14] J. H. Loxton and R. A. Smith, On Hua's estimate for exponential sums, J. London Math. Soc. (2) 26 (1982), 15-20. | Zbl 0474.10030
[014] [15] J. H. Loxton and R. C. Vaughan, The estimation of complete exponential sums, Canad. Math. Bull. 28 (1985), 442-454. | Zbl 0575.10033
[015] [16] V. I. Nechaev, An estimate of a complete rational trigonometric sum, Mat. Zametki 17 (1975), 839-849 (in Russian); English transl.: Math. Notes 17 (1975).
[016] [17] H. Salié, Über die Kloostermanschen Summen S(u,v;q), Math. Z. 34 (1931), 91-109.
[017] [18] W. M. Schmidt, Equations over Finite Fields, Lecture Notes in Math. 536, Springer, Berlin, 1976. | Zbl 0329.12001
[018] [19] R. A. Smith, Estimate for exponential sums, Proc. Amer. Math. Soc. 79 (1980), 365-368. | Zbl 0434.10026
[019] [20] S. B. Stechkin, Estimate of a complete rational trigonometric sum, Trudy Mat. Inst. Steklov. 143 (1977), 188-220 (in Russian); English transl.: Proc. Steklov Inst. Math. 1 (1980), 201-220. | Zbl 0433.10026
[020] [21] A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 203-210. | Zbl 0032.26102