On the estimation of certain exponential sums

E. Bombieri; S. Sperber

Acta Arithmetica (1995)

  • Volume: 69, Issue: 4, page 329-358
  • ISSN: 0065-1036

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E. Bombieri, and S. Sperber. "On the estimation of certain exponential sums." Acta Arithmetica 69.4 (1995): 329-358. <http://eudml.org/doc/206691>.

@article{E1995,
author = {E. Bombieri, S. Sperber},
journal = {Acta Arithmetica},
keywords = {exponential sums; finite field; quasi-projective variety},
language = {eng},
number = {4},
pages = {329-358},
title = {On the estimation of certain exponential sums},
url = {http://eudml.org/doc/206691},
volume = {69},
year = {1995},
}

TY - JOUR
AU - E. Bombieri
AU - S. Sperber
TI - On the estimation of certain exponential sums
JO - Acta Arithmetica
PY - 1995
VL - 69
IS - 4
SP - 329
EP - 358
LA - eng
KW - exponential sums; finite field; quasi-projective variety
UR - http://eudml.org/doc/206691
ER -

References

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  1. [AS1] A. Adolphson and S. Sperber, Exponential sums and Newton polyhedra: Cohomology and estimates, Ann. of Math. 130 (1989), 367-406. Zbl0723.14017
  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 𝔾ⁿₘ, Invent. Math. 101 (1990), 63-79. Zbl0764.11037
  4. [Ar] M. Artin, On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966), 129-136. Zbl0142.18602
  5. [B1] E. Bombieri, On exponential sums in finite fields, Amer. J. Math. 88 (1966), 71-105. Zbl0171.41504
  6. [B2] E. Bombieri, On exponential sums in finite fields II, Invent. Math. 47 (1978), 29-39. Zbl0396.14001
  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. Zbl0647.14007
  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. Zbl0763.14025
  11. [Ha] H. Hasse, Theorie der relativ-zyklischen algebraischen Funktionenkörper, insbesondere bei endlichem Konstantenkörper, J. Reine Angew. Math. 172 (1934), 37-54. Zbl60.0097.01
  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. Zbl0702.11034
  14. [K] N. Katz, Sommes exponentielles (rédigé par G. Laumon ), Astérisque 79 (1980). Zbl0469.12007
  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. Zbl0058.27202
  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). Zbl0057.28101
  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. Zbl0036.16001

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