@article{JTNB_1990__2_2_431_0, author = {Jean-Marc Deshouillers}, 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}, zbl = {0716.11047}, mrnumber = {1081735}, language = {en}, url = {https://jtnb.centre-mersenne.org/item/JTNB_1990__2_2_431_0/} }
TY - JOUR AU - Jean-Marc Deshouillers TI - Study of rational cubic forms via the circle method [after D.R. Heath-Brown, C. Hooley, and R.C. Vaughan] JO - Journal de théorie des nombres de Bordeaux PY - 1990 SP - 431 EP - 450 VL - 2 IS - 2 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/item/JTNB_1990__2_2_431_0/ LA - en ID - JTNB_1990__2_2_431_0 ER -
%0 Journal Article %A Jean-Marc Deshouillers %T Study of rational cubic forms via the circle method [after D.R. Heath-Brown, C. Hooley, and R.C. Vaughan] %J Journal de théorie des nombres de Bordeaux %D 1990 %P 431-450 %V 2 %N 2 %I Université Bordeaux I %U https://jtnb.centre-mersenne.org/item/JTNB_1990__2_2_431_0/ %G en %F JTNB_1990__2_2_431_0
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. https://jtnb.centre-mersenne.org/item/JTNB_1990__2_2_431_0/
Diagonal cubic equations II, Acta Arith. 53 (1989), 217-250. | MR | Zbl
, 1988,The addition of norm forms Mathematika. 9 (1962), 75-82. | MR | Zbl
, , , 1962,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).
, 1989,The distribution of Galois groups and Hilbert's irreducibility theorem, Proc. London Math. Soc (3) 43 (1981), 227-250. | MR | Zbl
, 1979,Arithmétique des variétés rationnelles et problèmes birationnels, Proc. Int. Congress Math. (1987), 641-653. | MR | Zbl
, 1986,Intersection of two quadrics and Châtelet surfaces, II, J. reine ang. Math. 374 (1987), 72-168. | MR | Zbl
, , , 1986,Arithmetic on some singular cubic hypersurfaces, Proc. London Math. Soc. (3) 58 (1989), 519-549. | MR | Zbl
, , 1988,Analytic methods for Diophantine equations and Diophantine inequalities, Univ. Michigan, (1962). | MR | Zbl
, 1962,Cubic forms in sixteen variables, Proc. Roy. Soc. London ser. A, 272 (1963), 285-303. | MR | Zbl
,La conjoncture de Weil, I, Pub. Math. 43 (IHES, Paris, 1974), 273-307.. | Numdam | MR | Zbl
,Problème de Waring pour les bicarrés, Sém. Th. Nb. Bordeaux (1984-1985), exposé 14, 47 p. | MR
, 1985,Divisors, Cambridge University Press. | MR | Zbl
, , 1988,cf. several papers on Partitio Numerorum, in G.H. I-IARDY's collected papers, Oxford, (1966).
, , 1919-1928,Asymptotic formulae in combinatory analysis, Proc. London Math. Soc. (2), 17 (1918), 75-115. | JFM
, , 1917,Cubic forms in ten variables, Proc. London Math. Soc. (3), 47 (1983), 225-257. | MR | Zbl
, 1982,On a new technique and its applications to the theory of numbers, Proc. London Math. Soc. (3), 38 (1979), 115-151. | MR | Zbl
, 1977,On Waring's problem, Acta Math. 157 (1986), 49-97. | MR | Zbl
, 1984,On nonary cubic forms, J. reine ang. Math. 386 (1988), 32-98. | MR | Zbl
, 1987,On sums of two norms from cubic field, in Journées de Théorie additive des Nombres (Université Bordeaux I, 1977). | MR | Zbl
, 1977,Perversity and exponential sums. à paraître
,On the representation of numbers in the form ax2 + by2 + cz2 + dt2, Acta Math. 49 (1926), 407-464. | JFM
, 1925,On the representation of numbers in the form ax2 + by2 + cz2 + dt2, Proc. London Math. Soc. (2) 25 (1926), 143-173. | JFM
, 1925,Une présentation adélique de la série singulière et du problème de Waring, Ens. Math. 28 (1982), 139-169. | MR | Zbl
, 1982,On the represention of large numbers as sums of seven cubes, Doklady Akad. Nauk SSSR 12 (1943), 218-224. | MR | Zbl
,A remark on indeterminate forms in several variables, J. London Math. Soc. 12 (1937), 127-129. | JFM | Zbl
1936,Topics in Analytic Number Theory, Springer- Verlag. | MR | Zbl
, 1969,Some remarks on Weyl sums, Coll. Math. Soc. Janos Bolyai 34 (Halasz ed.) Amsterdam (1984), 1585-1602. | MR | Zbl
, 1981,The Hardy-Littlewood method, Cambridge (1981). | MR | Zbl
, 1981,On Waring's problem for cubes, J. reine ang. Math. 365 (1986), 122-170, | MR | Zbl
, 1985,On Waring's problem for cubes, II, J. London Math. Soc. 39 (1989), 205-218. | MR | Zbl
, 1987,Uber die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352. | JFM | MR
, 1914,