@article{ASNSP_1992_4_19_1_113_0, 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}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_1992_4_19_1_113_0/} }
TY - JOUR AU - Deshouillers, Jean-Marc AU - Dress, François TI - Sums of 19 biquadrates : on the representation of large integers JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1992 SP - 113 EP - 153 VL - 19 IS - 1 PB - Scuola normale superiore UR - http://archive.numdam.org/item/ASNSP_1992_4_19_1_113_0/ LA - en ID - ASNSP_1992_4_19_1_113_0 ER -
%0 Journal Article %A Deshouillers, Jean-Marc %A Dress, François %T Sums of 19 biquadrates : on the representation of large integers %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1992 %P 113-153 %V 19 %N 1 %I Scuola normale superiore %U http://archive.numdam.org/item/ASNSP_1992_4_19_1_113_0/ %G en %F ASNSP_1992_4_19_1_113_0
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, Série 4, Tome 19 (1992) no. 1, pp. 113-153. http://archive.numdam.org/item/ASNSP_1992_4_19_1_113_0/
[1] On Waring's problem for biquadrates. Proc. Nat. Acad. Sci. India Sect. A 11 (1940), 437-450. | MR | Zbl
,[2] On Waring's problem: g(4) ≤ 21. Hardy-Ramanujan Journ. 2 (1979), 1-31. | Zbl
,[3] On Waring's problem: g(4) ≤ 20. Hardy-Ramanujan Journ. 8 (1985), 1-40. | Zbl
,[4] Problème de Waring pour les bicarrés, 1: Schéma de la solution. C.R. Acad. Sci. Paris 303 (1986), 85-88. | MR | Zbl
- - ,[5] 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] Number Theory. Acad. Press, New York, 1966. | MR | Zbl
- ,[7] RUN, Waring's problem for g(5) = 37. Sci. Sinica 13 (1964), 1547-1568. | MR | Zbl
-[8] Sur les sommes de puissances entières. C.R. Acad. Sci. Paris 207 (1938), 1366-1368. | JFM | Zbl
,[9] On Waring's problem for fourth powers. Ann. of Math. 40 (1939), 731-747. | JFM | MR | Zbl
,[10] On the computation of g(k) in Waring's problem. Math. Comp. 54 (1990), 815-820. | MR | Zbl
- ,[11] Problème de Waring pour les bicarrés. Sém. Th. Nb. Bordeaux, année 1984- 1985, exp. 14, 47 pp. | EuDML | MR | Zbl
,[12] Le problème de Waring pour les bicarrés: le point en 1984. Sém. Th. anal. Nb. Paris, année 1984-1985. | EuDML | Numdam | MR | Zbl
,[13] Sommes de diviseurs et structures multiplicatives des entiers. Acta Arith. 49 (1988), 341-375. | EuDML | MR | Zbl
- ,[14] Sur la majoration de sommes de Weyl biquadratiques (to appear Annali Scuola Normale Superiore Pisa). | EuDML | Numdam | MR | Zbl
,[15] Numerical results for sums of 5 and 7 biquadrates, and consequences for sums of 19 biquadrates (submitted to Math. Comp.). | Zbl
- ,[16] 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] Some problems in "Partitio Numerorum" (VI): Further researches omn Waring's problem. Math. Z. 23 (1925), 1-37. | EuDML | JFM | MR
- ,[18] KENG, On Waring's problem. Quart. Journ. Math. 9 (1938), 199-202. | JFM | Zbl
-[19] Moyennes de fonctions arithmétiques sur des suites de faible densité. Thèse 3ème cycle, Université Bordeaux I, 1987.
,[20] 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] On Waring's problem. Journ. Indian Math. Soc. 2 (1936), 16-44. | JFM | Zbl
,[22] Approximate formulas for some functions of prime numbers. Ill. Journ. Math. 6 (1962), 64-94. | MR | Zbl
- ,[23] A numerical approach to Waring's problem for fourth powers. Ph.D. thesis, University of Michigan, 1973.
,[24] Waring's problem for 22 biquadrates. Trans. Amer. Math. Soc. 193 (1974), 427-430. | MR | Zbl
,[25] The Theory of the Riemann Zeta Function. Clarendon Press, Oxford, 1951. | MR | Zbl
,[26] A new solution of Waring's problem. Dokl. Akad. Nank SSSR(1934), vol. 2, 337-341. | JFM | Zbl
,[27] On the upper bound of G(n) in Waring's problem. Izv. Akad. Nauk SSSR 10 (1934), 1455-1469. | JFM
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