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ArticleOriginal scientific text

Title

Pure and mixed exponential sums

Authors 1, 2

Affiliations

  1. Department of Mathematics, Kansas State University, Manhattan, KS 66506, U.S.A.
  2. Department of Mathematics, Zhongshan University, Guangzhou, P.R. China

Keywords

ENG
exponential sums

Bibliography

  1. E. Bombieri, On exponential sums in finite fields, Amer. J. Math. 88 (1966), 71-105.
  2. J. H. H. Chalk, On Hua's estimate for exponential sums, Mathematika 34 (1987), 115-123.
  3. J. R. Chen, On Professor Hua's estimate of exponential sums, Sci. Sinica 20 (1977), 711-719.
  4. T. Cochrane and Z. Y. Zheng, Exponential sums with rational function entries, to appear.
  5. P. Ding, An improvement to Chalk's estimation of exponential sums, Acta Arith. 59 (1991), 149-155.
  6. P. Ding, On a conjecture of Chalk, J. Number Theory 65 (1997), 116-129.
  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.
  8. G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio Numerorum', Math. Z. 23 (1925), 1-37.
  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.
  10. L. K. Hua, On exponential sums, J. Chinese Math. Soc. 20 (1940), 301-312.
  11. L. K. Hua, On exponential sums, Sci. Record (Peking) (N.S.) 1 (1957), 1-4.
  12. L. K. Hua, Additive Primzahltheorie, Teubner, Leipzig, 1959, 2-7.
  13. W. K. A. Loh, Hua's Lemma, Bull. Austral. Math. Soc. (3) 50 (1994), 451-458.
  14. J. H. Loxton and R. A. Smith, On Hua's estimate for exponential sums, J. London Math. Soc. (2) 26 (1982), 15-20.
  15. J. H. Loxton and R. C. Vaughan, The estimation of complete exponential sums, Canad. Math. Bull. 28 (1985), 442-454.
  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).
  17. H. Salié, Über die Kloostermanschen Summen S(u,v;q), Math. Z. 34 (1931), 91-109.
  18. W. M. Schmidt, Equations over Finite Fields, Lecture Notes in Math. 536, Springer, Berlin, 1976.
  19. R. A. Smith, Estimate for exponential sums, Proc. Amer. Math. Soc. 79 (1980), 365-368.
  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.
  21. A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 203-210.
Acta Arithmetica
1999/91/3
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Pages:
249-278
Main language of publication
English
Received
1999-01-04
Accepted
1999-05-20
Published
1999
Exact and natural sciences