Study of rational cubic forms via the circle method [after D.R. Heath-Brown, C. Hooley, and R.C. Vaughan]
Séminaire de théorie des nombres de Bordeaux, Série 2, Tome 2 (1990) no. 2, pp. 431-450. 
@article{JTNB_1990__2_2_431_0,
     author = {Deshouillers, Jean-Marc},
     title = {Study of rational cubic forms via the circle method [after {D.R.} {Heath-Brown,} {C.} {Hooley,} and {R.C.} {Vaughan]}},
     journal = {S\'eminaire de th\'eorie des nombres de Bordeaux},
     pages = {431--450},
     publisher = {Universit\'e Bordeaux I},
     volume = {Ser. 2, 2},
     number = {2},
     year = {1990},
     mrnumber = {1081735},
     zbl = {0716.11047},
     language = {en},
     url = {http://archive.numdam.org/item/JTNB_1990__2_2_431_0/}
}
TY  - JOUR
AU  - Deshouillers, Jean-Marc
TI  - Study of rational cubic forms via the circle method [after D.R. Heath-Brown, C. Hooley, and R.C. Vaughan]
JO  - Séminaire de théorie des nombres de Bordeaux
PY  - 1990
SP  - 431
EP  - 450
VL  - 2
IS  - 2
PB  - Université Bordeaux I
UR  - http://archive.numdam.org/item/JTNB_1990__2_2_431_0/
LA  - en
ID  - JTNB_1990__2_2_431_0
ER  - 
%0 Journal Article
%A Deshouillers, Jean-Marc
%T Study of rational cubic forms via the circle method [after D.R. Heath-Brown, C. Hooley, and R.C. Vaughan]
%J Séminaire de théorie des nombres de Bordeaux
%D 1990
%P 431-450
%V 2
%N 2
%I Université Bordeaux I
%U http://archive.numdam.org/item/JTNB_1990__2_2_431_0/
%G en
%F JTNB_1990__2_2_431_0
Deshouillers, Jean-Marc. Study of rational cubic forms via the circle method [after D.R. Heath-Brown, C. Hooley, and R.C. Vaughan]. Séminaire de théorie des nombres de Bordeaux, Série 2, Tome 2 (1990) no. 2, pp. 431-450. http://archive.numdam.org/item/JTNB_1990__2_2_431_0/

R.C. Baker, 1988, Diagonal cubic equations II, Acta Arith. 53 (1989), 217-250. | MR | Zbl

B.J. Birch, H. Davenport, D.J. Lewis, 1962, The addition of norm forms Mathematika. 9 (1962), 75-82. | MR | Zbl

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).

S.D. Cohen, 1979, The distribution of Galois groups and Hilbert's irreducibility theorem, Proc. London Math. Soc (3) 43 (1981), 227-250. | MR | Zbl

J.-L. Colliot-Thelene, 1986, Arithmétique des variétés rationnelles et problèmes birationnels, Proc. Int. Congress Math. (1987), 641-653. | MR | Zbl

J.-L. Colliot-Thelene, J. Sansuc, Sir P. Swinnerton-Dyer, 1986, Intersection of two quadrics and Châtelet surfaces, II, J. reine ang. Math. 374 (1987), 72-168. | MR | Zbl

J.-L. Colliot-Thelene, P. Salberger, 1988, Arithmetic on some singular cubic hypersurfaces, Proc. London Math. Soc. (3) 58 (1989), 519-549. | MR | Zbl

H. Davenport, 1962, Analytic methods for Diophantine equations and Diophantine inequalities, Univ. Michigan, (1962). | MR | Zbl

H. Davenport, Cubic forms in sixteen variables, Proc. Roy. Soc. London ser. A, 272 (1963), 285-303. | MR | Zbl

P. Deligne, La conjoncture de Weil, I, Pub. Math. 43 (IHES, Paris, 1974), 273-307.. | Numdam | MR | Zbl

J.-M. Deshouillers, 1985, Problème de Waring pour les bicarrés, Sém. Th. Nb. Bordeaux (1984-1985), exposé 14, 47 p. | MR

R.R. Hall, G. Tenenbaum, 1988, Divisors, Cambridge University Press. | MR | Zbl

G.H. Hardy, J.E. Littlewood, 1919-1928, cf. several papers on Partitio Numerorum, in G.H. I-IARDY's collected papers, Oxford, (1966).

G.H. Hardy, S. Ramanujan, 1917, Asymptotic formulae in combinatory analysis, Proc. London Math. Soc. (2), 17 (1918), 75-115. | JFM

D.R. Heath-Brown, 1982, Cubic forms in ten variables, Proc. London Math. Soc. (3), 47 (1983), 225-257. | MR | Zbl

C. Hooley, 1977, On a new technique and its applications to the theory of numbers, Proc. London Math. Soc. (3), 38 (1979), 115-151. | MR | Zbl

C. Hooley, 1984, On Waring's problem, Acta Math. 157 (1986), 49-97. | MR | Zbl

C. Hooley, 1987, On nonary cubic forms, J. reine ang. Math. 386 (1988), 32-98. | MR | Zbl

H. Iwaniec, 1977, On sums of two norms from cubic field, in Journées de Théorie additive des Nombres (Université Bordeaux I, 1977). | MR | Zbl

N.M. Katz, Perversity and exponential sums. à paraître

H.D. Kloosterman, 1925, On the representation of numbers in the form ax2 + by2 + cz2 + dt2, Acta Math. 49 (1926), 407-464. | JFM

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. | JFM

G. Lachaud, 1982, Une présentation adélique de la série singulière et du problème de Waring, Ens. Math. 28 (1982), 139-169. | MR | Zbl

Ju.V. Linnik, On the represention of large numbers as sums of seven cubes, Doklady Akad. Nauk SSSR 12 (1943), 218-224. | MR | Zbl

L.J. Mordell 1936, A remark on indeterminate forms in several variables, J. London Math. Soc. 12 (1937), 127-129. | JFM | Zbl

H. Rademacher, 1969, Topics in Analytic Number Theory, Springer- Verlag. | MR | Zbl

R.C. Vaughan, 1981, Some remarks on Weyl sums, Coll. Math. Soc. Janos Bolyai 34 (Halasz ed.) Amsterdam (1984), 1585-1602. | MR | Zbl

R.C. Vaughan, 1981, The Hardy-Littlewood method, Cambridge (1981). | MR | Zbl

R.C. Vaughan, 1985, On Waring's problem for cubes, J. reine ang. Math. 365 (1986), 122-170, | MR | Zbl

R.C. Vaughan, 1987, On Waring's problem for cubes, II, J. London Math. Soc. 39 (1989), 205-218. | MR | Zbl

H. Weyl, 1914, Uber die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352. | JFM | MR