L'étude des formes cubiques rationnelles via la méthode du cercle

Jean-Marc Deshouillers

Séminaire Bourbaki (1989-1990)

  • Volume: 32, page 155-177
  • ISSN: 0303-1179

How to cite

top

Deshouillers, Jean-Marc. "L'étude des formes cubiques rationnelles via la méthode du cercle." Séminaire Bourbaki 32 (1989-1990): 155-177. <http://eudml.org/doc/110122>.

@article{Deshouillers1989-1990,
author = {Deshouillers, Jean-Marc},
journal = {Séminaire Bourbaki},
keywords = {applications of Hardy-Littlewood circle method; cubic forms; Waring's problem for cubes},
language = {fre},
pages = {155-177},
publisher = {Société Mathématique de France},
title = {L'étude des formes cubiques rationnelles via la méthode du cercle},
url = {http://eudml.org/doc/110122},
volume = {32},
year = {1989-1990},
}

TY - JOUR
AU - Deshouillers, Jean-Marc
TI - L'étude des formes cubiques rationnelles via la méthode du cercle
JO - Séminaire Bourbaki
PY - 1989-1990
PB - Société Mathématique de France
VL - 32
SP - 155
EP - 177
LA - fre
KW - applications of Hardy-Littlewood circle method; cubic forms; Waring's problem for cubes
UR - http://eudml.org/doc/110122
ER -

References

top
  1. [1] R.C. Baker, 1988 - Diagonal cubic equations, II, Acta Arithmetica53 (1989) 217-250 Zbl0642.10041MR1032826
  2. [2] B.J. Birch, H. Davenport, D.J. Lewis, 1962 - The addition of norm formsMathematika9 (1962) 75-82. Zbl0105.02804MR144880
  3. [3] J. Cherly, 1989 - Sommes d'exponentielles cubiques dans l'anneau des polynômes en une variable sur le corps à deux éléments, et application au problème de Waring, Thèse de Doctorat d'Etat, Univ. Bordeaux I, 1989. 
  4. [4] S.D. Cohen, 1979 - The distribution of Galois groups and Hilbert's irreducibility theorem, Proc. London Math. Soc. (3), 43 (1981) 227- 250. Zbl0484.12002MR628276
  5. [5] J.-L. Colliot-Thélène, 1986 - Arithmétique des variétés rationnelles et problèmes birationnels, Proc. Int. Congress Math., (1987) 641-653. Zbl0698.14060MR934267
  6. [6] J.-L. Colliot-Thélène, J. Sansuc, Sir P. Swinnerton-Dyer, 1986 - Intersection of two quadrics and Châtelet surfaces, II, J. reine ang. Math.374 (1987) 72-168. Zbl0622.14030MR876222
  7. [7] J.-L. Colliot-Thélène, P. Salberger, 1988 - Arithmetic on some singular cubic hypersurfaces. Proc. London Math. Soc. (3), 58 (1989) 519-549. Zbl0638.14011MR988101
  8. [8] H. Davenport, 1962 - Analytic methods for Diophantine equations and Diophantine inequalities, Univ. Michigan, 1962. Zbl1089.11500MR2152164
  9. [9] H. Davenport - Cubic forms in sixteen variables, Proc. Roy. Soc. London ser. A, 272 (1963) 285-303. Zbl0107.04102MR155800
  10. [10] P. Deligne - La conjecture de Weil, I, Pub. Math.43 (IHES, Paris, 1974) 273-307. Zbl0287.14001MR340258
  11. [11] J.-M. Deshouillers, 1985 - Problème de Waring pour les bicarrés, Sem. Th. Nb. Bordeaux (1984-1985), exposé 14, 47 p. MR848372
  12. [12] R.R. Hall, G. Tenenbaum, 1988 - Divisors, Cambridge University Press. Zbl0653.10001MR964687
  13. [13] G.H. Hardy, J.E. Littlewood, 1919-1928 - cf. Several papers on Partitio Numerorum, in G.H. HARDY's collected papers, Oxford, 1966. 
  14. [14] G.H. Hardy, S. Ramanujan, 1917 - Asymptotic formule in combinatory analysis, Proc. London Math. Soc. (2), 17 (1918) 75-115. Zbl46.0198.04JFM46.0198.04
  15. [15] D.R. Heath-Brown, 1982 - Cubic forms in ten variables, Proc. London Math. Soc. (3), 47 (1983) 225-257. Zbl0494.10012MR703978
  16. [16] C. Hooley, 1977 - On a new technique and its applications to the theory of numbers, Proc. London Math. Soc. (3), 38 (1979) 115-151. Zbl0394.10027MR520975
  17. [17] C. Hooley, 1984 - On Waring's problem, Acta Math.157 (1986) 49-97. Zbl0614.10038
  18. [18] C. Hooley, 1987 - On nonary cubic forms, J. reine ang. Math.386 (1988), 32-98. Zbl0641.10019MR936992
  19. [19] H. Iwaniec, 1977 - On sums of two norms from cubic fields, in Journées de théorie additive des nombres (Université de Bordeaux I, 1977) Zbl0521.10016MR614605
  20. [20] N.M. Katz, - Perversity and exponential sums, à paraître. Zbl0755.14008
  21. [21] H.D. Kloosterman, 1925 - On the representation of numbers in the form ax2 + by2 + cz2 + dt2. Acta Math.49 (1926) 407-464. JFM53.0155.01
  22. [22] H.D. Kloosterman, 1925 - On the representation of numbers in the form ax2 + by2 + cz2 + dt2. Proc. London Math. Soc. (2), 25 (1926) 143-173. JFM52.0170.02
  23. [23] G. Lachaud, 1982 - Une présentation adéligne de la série singulière et du problème de Waring, Ens. Math.28 (1982) 139-169. Zbl0499.12010MR670501
  24. [24] Ju.V. Linnik - On the representation of large numbers as sums of seven cubes. Doklady Akad. Nauk SSSR35 (1942), 162 and Mat. Sbornik12 (1943) 218-224. Zbl0063.03579MR9388
  25. [25] L.J. Mordell 1936 - A remarie on indeterminate forms in several variables, J. London Math. Soc.12 (1937) 127-129. JFM63.0116.03
  26. [26] H. Rademacher, 1969 - Topics in Analytic Number Theory, Springer-Verlag, 1973. Zbl0253.10002MR364103
  27. [27] R.G. Vaughan, 1981 - Some remarks on Weyl sums, Coll. Math. Soc. Janos Bolyai34 (Halasz ed.) Amsterdam, 1984, 1585-1602. Zbl0545.10024MR781198
  28. [28] R.G. Vaughan, 1981 - The Hardy-Littlewood method, Cambridge, 1981. Zbl0455.10034
  29. [29] R.G. Vaughan, 1985 - On Waring's problem for cubes, J. reine ang. Math.365 (1986) 122-170. Zbl0574.10046MR826156
  30. [30] R.G. Vaughan, 1987 - On Waring's problem for cubes, II, J. London Math. Soc.39 (1989) 205-218. Zbl0677.10034MR991656
  31. [31] H. Weyl, 1914 - Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann.77 (1916) 313-352. Zbl46.0278.06MR1511862JFM46.0278.06

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.