A sieve approach to the Waring-Goldbach problem, II On the seven cubes theorem

• Autorzy: Jörg Brüdern
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 72
• Numer: 3
• Strony: 211-227

Daty

wydano

1995

otrzymano

1994-10-05

Twórcy

autor

Jörg Brüdern

• Mathematisches Institut, A Pfaffenwaldring 57, 70551 Stuttgart, Germany

Bibliografia

• [1] J. Brüdern, On Waring's problem for fifth powers and some related topics, Proc. London Math. Soc. (3) 61 (1990), 457-479.
• [2] J. Brüdern, Sieves, the circle method, and Waring's problem for cubes, Habilitationsschrift, Göttingen 1991; Mathematica Gottingensis 51 (1991).
• [3] J. Brüdern, A note on cubic exponential sums, in: Séminaire de Théorie des Nombres, Paris 1990-91, S. David (ed.), Progr. Math. 108, Birkhäuser, Basel, 1992, 23-34.
• [4] J. Brüdern, A sieve approach to the Waring-Goldbach problem I: Sums of four cubes, Ann. Sci. École Norm. Sup. Paris, to appear.
• [5] J. Brüdern and E. Fouvry, Lagrange's four squares theorem with almost prime variables, J. Reine Angew. Math. 454 (1994), 59-96.
• [6] G. Greaves, A weighted sieve of Brun's type, Acta Arith. 40 (1981), 297-332.
• [7] L. K. Hua, Some results in additive prime number theory, Quart. J. Math. Oxford 9 (1938), 68-80.
• [8] L. K. Hua, Additive Theory of Prime Numbers, Providence, R. I., 1965.
• [9] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge University Press, 1981.
• [10] R. C. Vaughan, Some remarks on Weyl sums, in: Topics in Classical Number Theory, Colloq. Math. Soc. János Bolyai 34, North-Holland, Amsterdam, 1984.
• [11] R. C. Vaughan, On Waring's problem for cubes, J. Reine Angew. Math. 365 (1986), 121-170.
• [12] R. C. Vaughan, On Waring's problem for cubes II, J. London Math. Soc. (2) 39 (1989), 205-218.
• [13] R. C. Vaughan, A new iterative method in Waring's problem, Acta Math. 162 (1989), 1-71.
• [14] G. L. Watson, A proof of the seven cubes theorem, J. London Math. Soc. 26 (1951), 153-156.
• [15] T. D. Wooley, Large improvements in Waring's problem, Ann. of Math. 135 (1992), 131-146