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ArticleOriginal scientific text

Title

Exponential sums with rational function entries

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. K. E. Atkinson, An Introduction to Numerical Analysis, Wiley, New York, 1978.
  2. E. Bombieri, On exponential sums in finite fields, Amer. J. Math. 88 (1966), 71-105.
  3. L. Carlitz, A note on multiple Kloosterman sums, J. Indian Math. Soc. 29 (1965), 197-200.
  4. J. H. H. Chalk, On Hua's estimate for exponential sums, Mathematika 34 (1987), 115-123.
  5. J. R. Chen, On Professor Hua's estimate of exponential sums, Sci. Sinica 20 (1977), 711-719.
  6. T. Cochrane and Z. Y. Zheng, Pure and mixed exponential sums, Acta Arith. 91 (1999), 249-278.
  7. T. Cochrane and Z. Y. Zheng, On Hua's bound for exponential sums, preprint.
  8. P. Ding, An improvement to Chalk's estimation of exponential sums, Acta Arith. 59 (1991), 149-155.
  9. P. Ding, On a conjecture of Chalk, J. Number Theory 65 (1997), 116-129.
  10. W. Duke, J. Friedlander and H. Iwaniec, Bilinear forms with Kloosterman fractions, Invent. Math. 128 (1997), 23-43.
  11. T. Estermann, On Kloosterman's sum, Mathematika 8 (1961), 83-86.
  12. L. K. Hua, On exponential sums, J. Chinese Math. Soc. 20 (1940), 301-312.
  13. L. K. Hua, On exponential sums, Sci. Record (Peking) (N.S.) 1 (1957), 1-4.
  14. L. K. Hua, Additive Primzahltheorie, Teubner, Leipzig, 1959, 2-7.
  15. H. Iwaniec, Topics in Classical Automorphic Forms, Grad. Stud. Math. 17, Amer. Math. Soc., Providence, RI, 1991.
  16. N. Koblitz, p-adic Numbers, p-adic Analysis, and Zeta-Functions, 2nd ed., Springer, New York, 1984.
  17. S. V. Konyagin and I. E. Shparlinski, On the distribution of residues of finitely generated multiplicative groups and their applications, Macquarie Mathematics Reports, Macquarie University, 1995.
  18. W. K. A. Loh, Hua's Lemma, Bull. Austral. Math. Soc. 50 (1994), 451-458.
  19. W. K. A. Loh, Exponential sums on reduced residue systems, Canad. Math. Bull. 41 (1997), 187-195.
  20. J. H. Loxton and R. A. Smith, On Hua's estimate for exponential sums, J. London Math. Soc. (2) 26 (1982), 15-20.
  21. J. H. Loxton and R. C. Vaughan, The estimation of complete exponential sums, Canad. Math. Bull. 28 (1985), 442-454.
  22. 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).
  23. G. I. Perelmuter, Estimate of a sum along an algebraic curve, Mat. Zametki 5 (1969), 373-380 (in Russian).
  24. H. Salié, Über die Kloostermanschen Summen S(u,v;q), Math. Z. 34 (1931), 91-109.
  25. I. E. Shparlinski, On exponential sums with sparse polynomials and rational functions, J. Number Theory 60 (1996), 233-244.
  26. R. A. Smith, Estimate for exponential sums, Proc. Amer. Math. Soc. 79 (1980), 365-368.
  27. 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.
  28. A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 204-207.
  29. A. L. Whiteman, A note on Kloosterman's sums, Bull. Amer. Math. Soc. 51 (1945), 373-377.
  30. K. S. Williams, Note on the Kloosterman sum, Proc. Amer. Math. Soc. 30 (1971), 61-62.
Acta Arithmetica
2000/95/1
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Pages:
67-95
Main language of publication
English
Received
1999-11-08
Published
2000
Exact and natural sciences