Sums of 19 biquadrates : on the representation of large integers
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 19 (1992) no. 1, pp. 113-153.
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     author = {Deshouillers, Jean-Marc and Dress, Fran\c{c}ois},
     title = {Sums of 19 biquadrates : on the representation of large integers},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {113--153},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 19},
     number = {1},
     year = {1992},
     mrnumber = {1183760},
     zbl = {0769.11035},
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     url = {http://www.numdam.org/item/ASNSP_1992_4_19_1_113_0/}
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Deshouillers, Jean-Marc; Dress, François. Sums of 19 biquadrates : on the representation of large integers. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 19 (1992) no. 1, pp. 113-153. http://www.numdam.org/item/ASNSP_1992_4_19_1_113_0/

[1] F.C. Auluck, On Waring's problem for biquadrates. Proc. Nat. Acad. Sci. India Sect. A 11 (1940), 437-450. | MR | Zbl

[2] R. Balasubramanian, On Waring's problem: g(4) ≤ 21. Hardy-Ramanujan Journ. 2 (1979), 1-31. | Zbl

[3] R. Balasubramanian, On Waring's problem: g(4) ≤ 20. Hardy-Ramanujan Journ. 8 (1985), 1-40. | Zbl

[4] R. Balasubramanian - J-M. Deshouillers - F. Dress, Problème de Waring pour les bicarrés, 1: Schéma de la solution. C.R. Acad. Sci. Paris 303 (1986), 85-88. | MR | Zbl

[5] R. Balasubramanian - J-M. Deshouillers - F. Dress, Problème de Waring pour les bicarrés, 2: résultats auxiliaires pour le théorème asymptotique. C.R. Acad. Sci. Paris 303 (1986), 161-163. | MR | Zbl

[6] Z.I. Borevich - I.R. Shafarevich, Number Theory. Acad. Press, New York, 1966. | MR | Zbl

[7] Chen Jing- RUN, Waring's problem for g(5) = 37. Sci. Sinica 13 (1964), 1547-1568. | MR | Zbl

[8] H. Davenport, Sur les sommes de puissances entières. C.R. Acad. Sci. Paris 207 (1938), 1366-1368. | JFM | Zbl

[9] H. Davenport, On Waring's problem for fourth powers. Ann. of Math. 40 (1939), 731-747. | JFM | MR | Zbl

[10] F. Delmer - J-M. Deshouillers, On the computation of g(k) in Waring's problem. Math. Comp. 54 (1990), 815-820. | MR | Zbl

[11] J-M. Deshouillers, Problème de Waring pour les bicarrés. Sém. Th. Nb. Bordeaux, année 1984- 1985, exp. 14, 47 pp. | EuDML | MR | Zbl

[12] J-M. Deshouillers, Le problème de Waring pour les bicarrés: le point en 1984. Sém. Th. anal. Nb. Paris, année 1984-1985. | EuDML | Numdam | MR | Zbl

[13] J-M. Deshouillers - F. Dress, Sommes de diviseurs et structures multiplicatives des entiers. Acta Arith. 49 (1988), 341-375. | EuDML | MR | Zbl

[14] J-M. Deshouillers, Sur la majoration de sommes de Weyl biquadratiques (to appear Annali Scuola Normale Superiore Pisa). | EuDML | Numdam | MR | Zbl

[15] J-M. Deshouillers - F. Dress, Numerical results for sums of 5 and 7 biquadrates, and consequences for sums of 19 biquadrates (submitted to Math. Comp.). | Zbl

[16] L.E. Dickson, Proof of the ideal Waring theorem for exponents 7-180, followed by Solution of Waring's problem. Amer. Journ. Math. 58 (1936), 521-535. | JFM | MR | Zbl

[17] G.H. Hardy - J.E. Littlewood, Some problems in "Partitio Numerorum" (VI): Further researches omn Waring's problem. Math. Z. 23 (1925), 1-37. | EuDML | JFM | MR

[18] Hua Loo- KENG, On Waring's problem. Quart. Journ. Math. 9 (1938), 199-202. | JFM | Zbl

[19] B. Landreau, Moyennes de fonctions arithmétiques sur des suites de faible densité. Thèse 3ème cycle, Université Bordeaux I, 1987.

[20] V.I. Ne, V.L. Topunov, Estimation of the modulus of complete rational trigonometric sums of degree three and four (Russian). Trudy Mat. Inst. Steklov. 158 (1981), 125-129, 229. | MR | Zbl

[21] S.S. Pillai, On Waring's problem. Journ. Indian Math. Soc. 2 (1936), 16-44. | JFM | Zbl

[22] J.B. Rosser - L. Schoenfeld, Approximate formulas for some functions of prime numbers. Ill. Journ. Math. 6 (1962), 64-94. | MR | Zbl

[23] H.E. Thomas, A numerical approach to Waring's problem for fourth powers. Ph.D. thesis, University of Michigan, 1973.

[24] H.E. Thomas, Waring's problem for 22 biquadrates. Trans. Amer. Math. Soc. 193 (1974), 427-430. | MR | Zbl

[25] E.C. Titchmarsh, The Theory of the Riemann Zeta Function. Clarendon Press, Oxford, 1951. | MR | Zbl

[26] I.M. Vinogradov, A new solution of Waring's problem. Dokl. Akad. Nank SSSR(1934), vol. 2, 337-341. | JFM | Zbl

[27] I.M. Vinogradov, On the upper bound of G(n) in Waring's problem. Izv. Akad. Nauk SSSR 10 (1934), 1455-1469. | JFM