PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2000 | 95 | 1 | 67-95
Tytuł artykułu

Exponential sums with rational function entries

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
95
Numer
1
Strony
67-95
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-11-08
Twórcy
  • Department of Mathematics, Kansas State University, Manhattan, KS 66506, U.S.A.
  • Department of Mathematics, Zhongshan University, Guangzhou, P.R. China
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav95z1p67bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.