Pure and mixed exponential sums

• Autorzy: Todd Cochrane , Zhiyong Zheng
• Języki publikacji: EN

Słowa kluczowe

EN

exponential sums

Kategorie tematyczne

• 11L03: Trigonometric and exponential sums, general
• 11L07: Estimates on exponential sums

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 91
• Numer: 3
• Strony: 249-278

Daty

wydano

1999

otrzymano

1999-01-04

poprawiono

1999-05-20

Twórcy

autor

Todd Cochrane

• Department of Mathematics, Kansas State University, Manhattan, KS 66506, U.S.A.

autor

Zhiyong Zheng

• Department of Mathematics, Zhongshan University, Guangzhou, P.R. China

Bibliografia

• [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.