p-adic estimates for exponential sums and the theorem of Chevalley-Warning
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 20 (1987) no. 4, pp. 545-556.
@article{ASENS_1987_4_20_4_545_0,
     author = {Adolphson, Alan and Sperber, Steven},
     title = {$p$-adic estimates for exponential sums and the theorem of {Chevalley-Warning}},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {545--556},
     publisher = {Elsevier},
     volume = {Ser. 4, 20},
     number = {4},
     year = {1987},
     doi = {10.24033/asens.1543},
     mrnumber = {89d:11112},
     zbl = {0654.12011},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.1543/}
}
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Adolphson, Alan; Sperber, Steven. $p$-adic estimates for exponential sums and the theorem of Chevalley-Warning. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 20 (1987) no. 4, pp. 545-556. doi : 10.24033/asens.1543. http://www.numdam.org/articles/10.24033/asens.1543/

[1] A. Adolphson and S. Sperber, Exponential Sums on the Complement of a Hypersurface (Amer. J. Math., Vol. 102, 1980, pp. 461-487). | MR | Zbl

[2] A. Adolphson and S. Sperber, On the degree of the L-function associated with an exponential sum (to appear).

[3] A. Adolphson and S. Sperber, Newton Polyhedra and the Degree of the L-Function Associated to an Exponential Sum (Invent. Math., Vol. 88, 1987, pp. 555-569). | EuDML | MR | Zbl

[4] J. Ax, Zeroes of Polynomials over Finite Fields (Amer. J. Math., Vol. 86, 1964, pp. 255-261). | MR | Zbl

[5] P. Cassou-Noguès, Séries de Dirichlet et intégrales associées à un polynôme à deux indéterminées (J. of Number Theory, Vol. 23, 1986, pp. 1-54). | MR | Zbl

[6] P. Deligne, Cohomologie des intersections complètes in Groupes de Monodromie en Géométrie Algébrique (SGA 7 II) (Lecture Notes in Math., No. 340, P. Deligne and N. Katz, pp. 39-61, Berlin-Heidelberg - New York - Tokyo, Springer, 1973). | MR | Zbl

[7] B. Dwork, On the Zeta Function of a Hypersurface (Publ. Math. I.H.E.S., Vol. 12, 1962, pp. 5-68). | EuDML | Numdam | MR | Zbl

[8] B. Dwork, On the Zeta Function of a Hypersurface, II (Ann. of Math., Vol. 80, 1964, pp. 227-299). | MR | Zbl

[9] F. Ehlers and K.-C. Lo, Minimal Characteristic Exponent of the Gauss-Manin Connection of Isolated Singular Point and Newton Polyhedron (Math. Ann., Vol. 259, 1982, pp. 431-441). | EuDML | MR | Zbl

[10] N. Katz, On a theorem of Ax (Amer. J. Math., Vol. 93, 1971, pp. 485-499). | MR | Zbl

[11] A. G. Kouchnirenko, Polyèdres de Newton et nombres de Milnor (Invent. Math., Vol. 32, 1976, pp. 1-31). | MR | Zbl

[12] B. Lichtin and D. Meuser, Poles of a Local Zeta Function and Newton Polygons (Comp. Math., Vol. 55, 1985, pp. 313-332). | Numdam | MR | Zbl

[13] B. Mazur, Frobenius and the Hodge filtration (estimates) (Ann. of Math., Vol. 98, 1973, pp. 58-95). | MR | Zbl

[14] P. Monsky, p-Adic Analysis and Zeta Functions (Lectures in Mathematics, Kyoto University, Tokyo, Kinokuniya Bookstore). | Zbl

[15] J.-P. Serre, Endomorphismes complètement continus des espaces de Banach p-adiques (Publ. Math. I.H.E.S., Vol. 12, 1962, p. 69-85). | Numdam | MR | Zbl

[16] S. Sperber, On the p-Adic Theory of Exponential Sums (Amer. J. Math., Vol. 108, 1986, pp. 255-296). | MR | Zbl

[17] E. Warning, Bemerkung zur vorstehenden Arbeit von Herr Chevalley (Abh. Math. Sem. Univ. Hamburg, Vol. 11, 1936, pp. 76-83). | JFM | Zbl

[18] A. Weil, Number of Solutions of Equations in Finite Fields (Bull. Amer. Math. Soc., Vol. 55, 1949, pp. 497-508). | MR | Zbl

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