Problème de Waring pour les bicarrés : le point en 1984

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1. [1] Auluck ( F.C.). - On Waring's problem for biquadratics, Proc. Indian Acad. Sc., Section A, t. 11, 1940, p. 437-450. Zbl0061.07405MR2342
2. [2] Balasubramanian ( R.). - On Waring's problem : g(4) ≤ 21 , Hardy Ramanujan J., Bombay, t. 2, 1979, p. 3-31. Zbl0422.10045MR565299
3. [3] Davenport ( H.). - On Waring's problem for fourth powers, Annals of Math., Series 2, t. 40, 1939, p. 731-747. Zbl0024.01402MR253
4. [4] Davenport ( H.). - Analytic methods for diophantine equations and diophantine inequalities, the University of Michigan, fall semester, 1962. - Ann Arbor, Ann Arbor Publishers, 1963. Zbl1089.11500MR159786
5. [5] Dickson ( L.E.). - Recent progress on Waring's theorem and its generalizations, Bull. Amer. math. Soc., t. 39, 1933, p. 701-727. Zbl0008.00501
6. [6] Dress ( F.). - Amélioration de la majoration de g(4) dans le problème de Waring : g(4) ≤ 30 , Acta Arithm., Warszawa, t. 22, 1973, p. 137-147. Zbl0255.10047MR319887
7. [7] Ellison ( W.J.). - Waring's problem, Amer. math. Monthly, t. 78, 1971, p. 10- 36. Zbl0205.35001MR414510
8. [8] Hardy ( G.H. ) and Littlewood ( J.E.). - Some problems of "Partitio Numerorum", II : Proof that every large number is the sum of at most 21 biquadrates, Math. Z., t. 9, 1921, p. 14-27 ; VI : Further researches in Waring's problem, Math. Z., t. 23, 1925, p. 1-37. Zbl48.0142.01MR1544448JFM48.0142.01
9. [9] Hua ( L.-K.). - On Waring's problem, Quart. J. of Math., Oxford Series, t. 9, 1938, p. 199-202. Zbl0020.10504
10. [10] Kempner ( A.). - Bemerkungen zum Waringschen Problem, Math. Annalen, t. 72, 1912, p. 387-399. Zbl43.0239.02MR1511703JFM43.0239.02
11. [11] Liouville ( J.). - Lectures au Collège de France [voir LE BESGUE (V. A.). -Exercices d'analyse numérique, p. 112-115. - Paris, Leiber et Faraguet, 1859]. 
12. [12] Pillai ( S.S.). - On Waring's problem g(6) = 73 , Proc. Indian Acad. Sc., Section A, t. 12, 1940, p. 30-40. Zbl0025.30603MR2993
13. [13] Thomas ( H.E.). - A numerical approach to Waring's problem for fourth powers, the University of Michigan, Phil. Doct., 1973. 
14. [14] Thomas ( H.E.). - Waring's problem for twenty two biquadrates, Trans. Amer. math. Soc., t. 193, 1974, p. 427-430. Zbl0294.10033MR342478
15. [15] Vaughan ( R.C.). - The Hardy-Littlewood method. - Cambridge, New York, Melbourne, Cambridge University Press, 1981 (Cambridge Tracts in Mathematics, 80). Zbl0455.10034MR628618

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