Estimation of exponential sums of polynomials of higher degrees II

Yangbo Ye

Acta Arithmetica (2000)

  • Volume: 93, Issue: 3, page 221-235
  • ISSN: 0065-1036

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Yangbo Ye. "Estimation of exponential sums of polynomials of higher degrees II." Acta Arithmetica 93.3 (2000): 221-235. <http://eudml.org/doc/207412>.

@article{YangboYe2000,
author = {Yangbo Ye},
journal = {Acta Arithmetica},
keywords = {Davenport-Hasse identities; bounds for exponential sums; hyper-Kloosterman sums},
language = {eng},
number = {3},
pages = {221-235},
title = {Estimation of exponential sums of polynomials of higher degrees II},
url = {http://eudml.org/doc/207412},
volume = {93},
year = {2000},
}

TY - JOUR
AU - Yangbo Ye
TI - Estimation of exponential sums of polynomials of higher degrees II
JO - Acta Arithmetica
PY - 2000
VL - 93
IS - 3
SP - 221
EP - 235
LA - eng
KW - Davenport-Hasse identities; bounds for exponential sums; hyper-Kloosterman sums
UR - http://eudml.org/doc/207412
ER -

References

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  1. [1] R. Dąbrowski and B. Fisher, A stationary phase formula for exponential sums over / p m and applications to GL(3)-Kloosterman sums, Acta Arith. 80 (1997), 1-48. Zbl0893.11032
  2. [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. [3] N. M. Katz, Gauss Sums, Kloosterman Sums, and Monodromy Groups, Ann. of Math. Stud. 116, Princeton Univ. Press, Princeton, 1988. Zbl0675.14004
  4. [4] N. M. Katz, Exponential Sums and Differential Equations, Ann. of Math. Stud. 124, Princeton Univ. Press, Princeton, 1990. Zbl0731.14008
  5. [5] J. H. Loxton and R. A. Smith, On Hua's estimate for exponential sums, J. London Math. Soc. 26 (1982), 15-20. Zbl0474.10030
  6. [6] J. H. Loxton and R. C. Vaughan, The estimation of complete exponential sums, Canad. Math. Bull. 28 (1985), 440-454. Zbl0575.10033
  7. [7] R. A. Smith, On n-dimensional Kloosterman sums, J. Number Theory 11 (1979), 324-343. Zbl0409.10024
  8. [8] R. C. Vaughan, The Hardy-Littlewood Method, 2nd ed., Cambridge Tracts in Math. 125, Cambridge Univ. Press, Cambridge, 1997. Zbl0868.11046
  9. [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. Zbl0922.11068
  10. [10] Y. Ye, Hyper-Kloosterman sums and estimation of exponential sums of polynomials of higher degrees, Acta Arith. 86 (1998), 255-267. Zbl0923.11117

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