Hyper-Kloosterman sums and estimation of exponential sums of polynomials of higher degrees
Yangbo Ye
Acta Arithmetica, Tome 84 (1998), p. 255-267 / Harvested from The Polish Digital Mathematics Library
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Publié le : 1998-01-01
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     author = {Yangbo Ye},
     title = {Hyper-Kloosterman sums and estimation of exponential sums of polynomials of higher degrees},
     journal = {Acta Arithmetica},
     volume = {84},
     year = {1998},
     pages = {255-267},
     zbl = {0923.11117},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav86i3p255bwm}
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Yangbo Ye. Hyper-Kloosterman sums and estimation of exponential sums of polynomials of higher degrees. Acta Arithmetica, Tome 84 (1998) pp. 255-267. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav86i3p255bwm/

[000] [1] L. Carlitz and S. Uchiyama, Bounds for exponential sums, Duke Math. J. 24 (1957), 37-41. | Zbl 0088.03901

[001] [2] R. Dąbrowski and B. Fisher, A stationary phase formula for exponential sums over ℤ/pmℤ and applications to GL(3)-Kloosterman sums, Acta Arith. 80 (1997), 1-48. | Zbl 0893.11032

[002] [3] H. Davenport und H. Hasse, Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen, J. Reine Angew. Math. 172 (1935), 151-182. | Zbl 60.0913.01

[003] [4] 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.

[004] [5] L. K. Hua, On exponential sums, J. Chinese Math. Soc. 2 (1940), 301-312. | Zbl 0061.06608

[005] [6] N. M. Katz, Sommes exponentielles, Astérisque 79 (1980).

[006] [7] N. M. Katz, Gauss Sums, Kloosterman Sums, and Monodromy Groups, Ann. of Math. Stud. 116, Princeton Univ. Press, Princeton, 1988. | Zbl 0675.14004

[007] [8] N. M. Katz, Exponential Sums and Differential Equations, Ann. of Math. Stud. 124, Princeton Univ. Press, Princeton, 1990. | Zbl 0731.14008

[008] [9] J. H. Loxton and R. A. Smith, On Hua's estimate for exponential sums, J. London Math. Soc. 26 (1982), 15-20. | Zbl 0474.10030

[009] [10] J. H. Loxton and R. C. Vaughan, The estimation of complete exponential sums, Canad. Math. Bull. 28 (1985), 440-454. | Zbl 0575.10033

[010] [11] R. C. Vaughan, The Hardy-Littlewood Method, 2nd ed., Cambridge Tracts in Math. 125, Cambridge Univ. Press, Cambridge, 1997. | Zbl 0868.11046

[011] [12] Y. Ye, The lifting of an exponential sum to a cyclic algebraic number field of a prime degree, Trans. Amer. Math. Soc., to appear. | Zbl 0922.11068