Study of rational cubic forms via the circle method [after D.R. Heath-Brown, C. Hooley, and R.C. Vaughan]
Jean-Marc Deshouillers
Journal de Théorie des Nombres de Bordeaux, 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 = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {431--450},
     publisher = {Universit\'e Bordeaux I},
     volume = {2},
     number = {2},
     year = {1990},
     doi = {10.5802/jtnb.37},
     zbl = {0716.11047},
     mrnumber = {1081735},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.37/}
}
Jean-Marc Deshouillers. Study of rational cubic forms via the circle method [after D.R. Heath-Brown, C. Hooley, and R.C. Vaughan]. Journal de Théorie des Nombres de Bordeaux, Tome 2 (1990) no. 2, pp. 431-450. doi : 10.5802/jtnb.37. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.37/

R.C. Baker, 1988, Diagonal cubic equations II, Acta Arith. 53 (1989), 217-250. | MR 1032826 | Zbl 0642.10041

B.J. Birch, H. Davenport, D.J. Lewis, 1962, The addition of norm forms Mathematika. 9 (1962), 75-82. | MR 144880 | Zbl 0105.02804

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 628276 | Zbl 0484.12002

J.-L. Colliot-Thelene, 1986, Arithmétique des variétés rationnelles et problèmes birationnels, Proc. Int. Congress Math. (1987), 641-653. | MR 934267 | Zbl 0698.14060

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 876222 | Zbl 0622.14030

J.-L. Colliot-Thelene, P. Salberger, 1988, Arithmetic on some singular cubic hypersurfaces, Proc. London Math. Soc. (3) 58 (1989), 519-549. | MR 988101 | Zbl 0638.14011

H. Davenport, 1962, Analytic methods for Diophantine equations and Diophantine inequalities, Univ. Michigan, (1962). | MR 2152164 | Zbl 1089.11500

H. Davenport, Cubic forms in sixteen variables, Proc. Roy. Soc. London ser. A, 272 (1963), 285-303. | MR 155800 | Zbl 0107.04102

P. Deligne, La conjoncture de Weil, I, Pub. Math. 43 (IHES, Paris, 1974), 273-307.. | Numdam | MR 340258 | Zbl 0287.14001

J.-M. Deshouillers, 1985, Problème de Waring pour les bicarrés, Sém. Th. Nb. Bordeaux (1984-1985), exposé 14, 47 p. | MR 848372

R.R. Hall, G. Tenenbaum, 1988, Divisors, Cambridge University Press. | MR 964687 | Zbl 0653.10001

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 46.0198.04

D.R. Heath-Brown, 1982, Cubic forms in ten variables, Proc. London Math. Soc. (3), 47 (1983), 225-257. | MR 703978 | Zbl 0494.10012

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 520975 | Zbl 0394.10027

C. Hooley, 1984, On Waring's problem, Acta Math. 157 (1986), 49-97. | MR 857679 | Zbl 0614.10038

C. Hooley, 1987, On nonary cubic forms, J. reine ang. Math. 386 (1988), 32-98. | MR 936992 | Zbl 0641.10019

H. Iwaniec, 1977, On sums of two norms from cubic field, in Journées de Théorie additive des Nombres (Université Bordeaux I, 1977). | MR 614605 | Zbl 0521.10016

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 53.0155.01

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 52.0170.02

G. Lachaud, 1982, Une présentation adélique de la série singulière et du problème de Waring, Ens. Math. 28 (1982), 139-169. | MR 670501 | Zbl 0499.12010

Ju.V. Linnik, On the represention of large numbers as sums of seven cubes, Doklady Akad. Nauk SSSR 12 (1943), 218-224. | MR 9388 | Zbl 0063.03579

L.J. Mordell 1936, A remark on indeterminate forms in several variables, J. London Math. Soc. 12 (1937), 127-129. | JFM 63.0116.03 | Zbl 0017.00405

H. Rademacher, 1969, Topics in Analytic Number Theory, Springer- Verlag. | MR 364103 | Zbl 0253.10002

R.C. Vaughan, 1981, Some remarks on Weyl sums, Coll. Math. Soc. Janos Bolyai 34 (Halasz ed.) Amsterdam (1984), 1585-1602. | MR 781198 | Zbl 0545.10024

R.C. Vaughan, 1981, The Hardy-Littlewood method, Cambridge (1981). | MR 628618 | Zbl 0455.10034

R.C. Vaughan, 1985, On Waring's problem for cubes, J. reine ang. Math. 365 (1986), 122-170, | MR 826156 | Zbl 0574.10046

R.C. Vaughan, 1987, On Waring's problem for cubes, II, J. London Math. Soc. 39 (1989), 205-218. | MR 991656 | Zbl 0677.10034

H. Weyl, 1914, Uber die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352. | JFM 46.0278.06 | MR 1511862