Pure and mixed exponential sums

Todd Cochrane; Zhiyong Zheng

Acta Arithmetica (1999)

  • Volume: 91, Issue: 3, page 249-278
  • ISSN: 0065-1036

How to cite

top

Todd Cochrane, and Zhiyong Zheng. "Pure and mixed exponential sums." Acta Arithmetica 91.3 (1999): 249-278. <http://eudml.org/doc/207355>.

@article{ToddCochrane1999,
author = {Todd Cochrane, Zhiyong Zheng},
journal = {Acta Arithmetica},
keywords = {exponential sums; critical point; upper bounds; multiplicative character},
language = {eng},
number = {3},
pages = {249-278},
title = {Pure and mixed exponential sums},
url = {http://eudml.org/doc/207355},
volume = {91},
year = {1999},
}

TY - JOUR
AU - Todd Cochrane
AU - Zhiyong Zheng
TI - Pure and mixed exponential sums
JO - Acta Arithmetica
PY - 1999
VL - 91
IS - 3
SP - 249
EP - 278
LA - eng
KW - exponential sums; critical point; upper bounds; multiplicative character
UR - http://eudml.org/doc/207355
ER -

References

top
  1. [1] E. Bombieri, On exponential sums in finite fields, Amer. J. Math. 88 (1966), 71-105. Zbl0171.41504
  2. [2] J. H. H. Chalk, On Hua's estimate for exponential sums, Mathematika 34 (1987), 115-123. Zbl0621.10024
  3. [3] J. R. Chen, On Professor Hua's estimate of exponential sums, Sci. Sinica 20 (1977), 711-719. Zbl0374.10024
  4. [4] T. Cochrane and Z. Y. Zheng, Exponential sums with rational function entries, to appear. 
  5. [5] P. Ding, An improvement to Chalk's estimation of exponential sums, Acta Arith. 59 (1991), 149-155. Zbl0697.10031
  6. [6] P. Ding, On a conjecture of Chalk, J. Number Theory 65 (1997), 116-129. Zbl0876.11044
  7. [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. Zbl47.0114.02
  8. [8] G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio Numerorum', Math. Z. 23 (1925), 1-37. Zbl51.0148.01
  9. [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. Zbl0857.11041
  10. [10] L. K. Hua, On exponential sums, J. Chinese Math. Soc. 20 (1940), 301-312. Zbl0061.06608
  11. [11] L. K. Hua, On exponential sums, Sci. Record (Peking) (N.S.) 1 (1957), 1-4. Zbl0083.04204
  12. [12] L. K. Hua, Additive Primzahltheorie, Teubner, Leipzig, 1959, 2-7. 
  13. [13] W. K. A. Loh, Hua's Lemma, Bull. Austral. Math. Soc. (3) 50 (1994), 451-458. Zbl0833.11040
  14. [14] J. H. Loxton and R. A. Smith, On Hua's estimate for exponential sums, J. London Math. Soc. (2) 26 (1982), 15-20. Zbl0474.10030
  15. [15] J. H. Loxton and R. C. Vaughan, The estimation of complete exponential sums, Canad. Math. Bull. 28 (1985), 442-454. Zbl0575.10033
  16. [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. [17] H. Salié, Über die Kloostermanschen Summen S(u,v;q), Math. Z. 34 (1931), 91-109. 
  18. [18] W. M. Schmidt, Equations over Finite Fields, Lecture Notes in Math. 536, Springer, Berlin, 1976. Zbl0329.12001
  19. [19] R. A. Smith, Estimate for exponential sums, Proc. Amer. Math. Soc. 79 (1980), 365-368. Zbl0434.10026
  20. [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. Zbl0433.10026
  21. [21] A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 203-210. Zbl0032.26102

NotesEmbed ?

top

You must be logged in to post comments.