Sur certaines sommes d'exponentielles sur les nombres premiers

Étienne Fouvry; Philippe Michel

Annales scientifiques de l'École Normale Supérieure (1998)

  • Volume: 31, Issue: 1, page 93-130
  • ISSN: 0012-9593

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Fouvry, Étienne, and Michel, Philippe. "Sur certaines sommes d'exponentielles sur les nombres premiers." Annales scientifiques de l'École Normale Supérieure 31.1 (1998): 93-130. <http://eudml.org/doc/82457>.

@article{Fouvry1998,
author = {Fouvry, Étienne, Michel, Philippe},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {exponential sums; sums over prime numbers},
language = {fre},
number = {1},
pages = {93-130},
publisher = {Elsevier},
title = {Sur certaines sommes d'exponentielles sur les nombres premiers},
url = {http://eudml.org/doc/82457},
volume = {31},
year = {1998},
}

TY - JOUR
AU - Fouvry, Étienne
AU - Michel, Philippe
TI - Sur certaines sommes d'exponentielles sur les nombres premiers
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1998
PB - Elsevier
VL - 31
IS - 1
SP - 93
EP - 130
LA - fre
KW - exponential sums; sums over prime numbers
UR - http://eudml.org/doc/82457
ER -

References

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  1. [Ba-H] R. C. BAKER et G. HARMAN, On the distribution of {αpk} modulo 1, (Mathematika, vol. 38, 1991, p. 170-184). Zbl0751.11037MR92f:11096
  2. [Bo] E. BOMBIERI, Exponential sums in finite fields, (Amer. J. Math., vol. 88, 1966, p. 71-105). Zbl0171.41504MR34 #166
  3. [B-S] E. BOMBIERI et S. SPERBER, On the estimation of certain exponential sums, (Acta Arith., vol. 69, 1995, p. 329-358). Zbl0826.11040MR96d:11089
  4. [Da] H. DAVENPORT, Multiplicative Number Theory (Second Edition), (Graduate Texts in Mathematics, vol. 74, Springer Verlag, Berlin-Heidelberg-New York, 1980). Zbl0453.10002MR82m:10001
  5. [D-S] H. DAVENPORT et A. SCHINZEL, Two problems concerning polynomials, (J. reine angew. Math., vol. 214-215, 1964, p. 386-391). Zbl0152.02303MR29 #93
  6. [De1] P. DELIGNE, La Conjecture de Weil I, (Publ. de l'I.H.E.S., vol. 43, 1974, p. 273-308). Zbl0287.14001MR49 #5013
  7. [De2] P. DELIGNE, Applications de la Formule des Traces aux Sommes Trigonométriques, Séminaire de Géométrie Algébrique du Bois-Marie SGA41/2, Cohomologie Étale, (Lecture Notes in Mathematics, vol. 569, Springer Verlag, Berlin-Heidelberg-New York, 1977, p. 168-232). Zbl0349.10031
  8. [De3] P. DELIGNE, La Conjecture de Weil II, (Publ. de l'I.H.E.S., vol. 52, 1981, p. 313-428). 
  9. [Fo-1] E. FOUVRY et H. IWANIEC, The divisor function over arithmetic progressions, (with appendix by N. Katz), (Acta Arith., vol. 61, 1992, p. 271-287). Zbl0764.11040MR93g:11089
  10. [Fri] M. FRIED, The field of definition of function fields and a problem in the reduibility of polynomials in 2 variables, Ill. (J. Math., vol. 17, 1973, p. 128-144). Zbl0266.14013MR50 #329
  11. [Fr-I1] J. FRIEDLANDER et H. IWANIEC, Incomplete Kloosterman sums and a divisor problem, (Annals of Maths., vol. 121, 1985, p. 319-350). Zbl0572.10029MR86i:11050
  12. [Fr-I2] J. FRIEDLANDER et H. IWANIEC, Estimates for Character Sums, (Proc. Amer. Math. Soc., vol. 19, 1993, p. 365-372). Zbl0782.11022MR93k:11074
  13. [Gh] A. GHOSH, The Distribution of αp² modulo 1, (Proc. London Math. Soc., (3), vol. 42, 1981, p. 252-269). Zbl0397.10026MR82j:10067
  14. [Harm] G. HARMAN, Trigonometric Sums over Primes I, (Mathematika, vol. 28, 1981, p. 249-254). Zbl0465.10029MR83j:10045
  15. [Hart] R. HARTSHORNE, Algebraic Geometry, (Graduate Texts in Mathematics, vol. 52, Springer Verlag, Berlin-Heidelberg-New York, 1977). Zbl0367.14001MR57 #3116
  16. [Ho] C. HOOLEY, On exponential sums and certain of their applications, (Journées Arith. 1980, J.V. Armitage (ed), p. 92-122, Cambridge, 1982). Zbl0488.10041
  17. [Hu] L. K. HUA, Additive Theory of Prime Numbers, (Translations of Mathematical Monographs, vol. 13, American Math. Soc., 1965). Zbl0192.39304MR33 #2614
  18. [Ka1] N. M. KATZ, Gauss Sums, Kloosterman Sums and Monodromy Groups, (Annals of Maths. Studies, vol. 116, PUP). Zbl0675.14004MR91a:11028
  19. [Ka2] N. M. KATZ, Exponential sums and Differential Equations, (Annals of Maths. Studies, vol. 124, PUP). Zbl0731.14008MR93a:14009
  20. [Mi] P. MICHEL, Autour des Conjectures de Sato-Tate, (Thèse de Doctorat d'État, Université de Paris-Sud, Orsay, 1995). 
  21. [Mu] D. MUMFORD, The Red Book of Varieties and Schemes, (Lectures Notes in mathematics, vol. 1358, Springer Verlag, Berlin-Heidelberg-New York, 1988). Zbl0658.14001MR89k:14001
  22. [Schi1] A. SCHINZEL, Reducibility of polynomials in several variables, (Bull. Acad. Pol. Sci. Sér. Sci. Math. Astronom. Phys., vol. 11, 1963, p. 633-638). Zbl0122.01901MR28 #3032
  23. [Schi2] A. SCHINZEL, Reducibility of polynomials in several variables. II, (Pacific J. Math., vol. 118, 1985, p. 531-563). Zbl0571.12011MR86i:12005
  24. [Schm] W. SCHMIDT, Equations over finite fields : an elementary approach, (Lecture Notes in Mathematics, vol. 536, Springer Verlag, Berlin-Heidelberg-New York, 1976). Zbl0329.12001MR55 #2744
  25. [Va] R. C. VAUGHAN, Mean Value Theorems in Prime Number Theory, (J. London Math. Soc., (2), vol. 10, 1975, p. 153-162). Zbl0314.10028MR51 #12742
  26. [Vi] M. VINOGRADOV, The Method of Trigonometric Sum in the Theory of Numbers, Translated, revised and annotated by A. Davenport and K. F. Roth (Interscience, New York, 1954). Zbl0055.27504

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