ArticleOriginal scientific text

Title

On the estimation of certain exponential sums

Authors 1, 2

Affiliations

  1. Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A.
  2. School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.

Bibliography

  1. [AS1] A. Adolphson and S. Sperber, Exponential sums and Newton polyhedra: Cohomology and estimates, Ann. of Math. 130 (1989), 367-406.
  2. [AS2] A. Adolphson and S. Sperber, Exponential sums on (q), in: Proc. Conf. Automorphic Forms and Analytic Number Theory, CRM, Montreal, 1989, 1-6.
  3. [AS3] A. Adolphson and S. Sperber, Exponential sums on ⁿₘ, Invent. Math. 101 (1990), 63-79.
  4. [Ar] M. Artin, On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966), 129-136.
  5. [B1] E. Bombieri, On exponential sums in finite fields, Amer. J. Math. 88 (1966), 71-105.
  6. [B2] E. Bombieri, On exponential sums in finite fields II, Invent. Math. 47 (1978), 29-39.
  7. [BS] E. Bombieri and S. Sperber, On the degree of Artin L-functions in characteristic p, C. R. Acad. Sci. Paris Sér. I 306 (1988), 393-398.
  8. [D] P. Deligne, La conjecture de Weil II, Inst. Hautes Études Sci. Publ. Math. 82 (1981), 313-428.
  9. [DL1] J. Denef et F. Loeser, Polyèdres de Newton et poids de sommes exponentielles, in: p-Adic Analysis (Proceedings, Trento 1989), Lecture Notes in Math. 1454, Springer, Berlin, 217-222.
  10. [DL2] J. Denef et F. Loeser, Weights of exponential sums, intersection cohomology and Newton polyhedra, Invent. Math. 106 (1991), 275-294.
  11. [Ha] H. Hasse, Theorie der relativ-zyklischen algebraischen Funktionenkörper, insbesondere bei endlichem Konstantenkörper, J. Reine Angew. Math. 172 (1934), 37-54.
  12. [H] C. Hooley, On exponential sums and certain of their applications, in: Number Theory Days, 1980 (Exeter 1980), London Math Soc. Lecture Note Ser. 56, Cambridge Univ. Press, Cambridge, 1982, 92-122.
  13. [I] H. Iwaniec, Small eigenvalues of Laplacian for Γ₀(N), Acta Arith. 56 (1990), 65-82.
  14. [K] N. Katz, Sommes exponentielles (rédigé par G. Laumon ), Astérisque 79 (1980).
  15. [KL] N. Katz et G. Laumon, Transformation de Fourier et majoration des sommes exponentielles, Inst. Hautes Études Sci. Publ. Math. 62 (1986), 361-418.
  16. [L] S. Lang, Abelian Varieties, Interscience, New York, 1958.
  17. [LW] S. Lang and A. Weil, Number of points of varieties in finite fields, Amer. J. Math. 76 (1954), 819-827.
  18. [N] L. B. Nisnevich, On the number of points of an algebraic manifold in a prime finite field, Dokl. Akad. Nauk SSSR (N.S.) 99 (1954), 17-20 (in Russian).
  19. [R] M. Reid, Undergraduate Algebraic Geometry, London Math. Soc. Stud. Texts 12, Cambridge Univ. Press, 1988.
  20. [W] A. Weil, Sur les courbes algébriques et les variétés qui s'en déduisent, Publ. Inst. Math. Univ. Strasbourg, 1945. Also Actualités Sci. Indust. 1041, Hermann, Paris, 1948.
Pages:
329-358
Main language of publication
English
Received
1992-11-18
Accepted
1994-08-08
Published
1995
Exact and natural sciences