Estimation of exponential sums of polynomials of higher degrees II

• Autorzy: Yangbo Ye
• Języki publikacji: EN

Kategorie tematyczne

• 11L05: Gauss and Kloosterman sums; generalizations
• 11L07: Estimates on exponential sums

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 93
• Numer: 3
• Strony: 221-235

Daty

wydano

2000

otrzymano

1998-06-02

poprawiono

1999-11-09

Twórcy

autor

Yangbo Ye

• Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, U.S.A.

Bibliografia

• [1] R. Dąbrowski and B. Fisher, A stationary phase formula for exponential sums over $ℤ/p^mℤ$ and applications to GL(3)-Kloosterman sums, Acta Arith. 80 (1997), 1-48.
• [2] P. Deligne, Applications de la formule des traces aux sommes trigonométriques, in: Cohomologie Etale (SGA 4 1/2), Lecture Notes in Math. 569, Springer, Berlin, 1977, 168-232.
• [3] N. M. Katz, Gauss Sums, Kloosterman Sums, and Monodromy Groups, Ann. of Math. Stud. 116, Princeton Univ. Press, Princeton, 1988.
• [4] N. M. Katz, Exponential Sums and Differential Equations, Ann. of Math. Stud. 124, Princeton Univ. Press, Princeton, 1990.
• [5] J. H. Loxton and R. A. Smith, On Hua's estimate for exponential sums, J. London Math. Soc. 26 (1982), 15-20.
• [6] J. H. Loxton and R. C. Vaughan, The estimation of complete exponential sums, Canad. Math. Bull. 28 (1985), 440-454.
• [7] R. A. Smith, On n-dimensional Kloosterman sums, J. Number Theory 11 (1979), 324-343.
• [8] R. C. Vaughan, The Hardy-Littlewood Method, 2nd ed., Cambridge Tracts in Math. 125, Cambridge Univ. Press, Cambridge, 1997.
• [9] Y. Ye, The lifting of an exponential sum to a cyclic algebraic number field of a prime degree, Trans. Amer. Math. Soc. 350 (1998), 5003-5015.
• [10] Y. Ye, Hyper-Kloosterman sums and estimation of exponential sums of polynomials of higher degrees, Acta Arith. 86 (1998), 255-267.