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Tytuł artykułu

Further improvements in Waring's problem, IV: Higher powers

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
94
Numer
3
Strony
203-285
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-08-19
Twórcy
  • Department of Mathematics, McAllister Building, Pennsylvania State University, University Park, PA 16802, U.S.A.
autor
  • Department of Mathematics, University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, MI 48109-1109, U.S.A.
Bibliografia
  • [1] R. C. Baker, Diophantine Inequalities, Clarendon Press, Oxford, 1986.
  • [2] E. Bombieri and J. Pila, The number of integral points on arcs and ovals, Duke Math. J. 59 (1989), 337-357.
  • [3] J. Brüdern, A problem in additive number theory, Math. Proc. Cambridge Philos. Soc. 103 (1988), 27-33.
  • [4] J. Brüdern and T. D. Wooley, On Waring's problem for cubes and smooth Weyl sums, Proc. London Math. Soc., to appear.
  • [5] I. Danicic, Contributions to Number Theory, Ph.D. thesis, London, 1957.
  • [6] T. Estermann, Einige Sätze über quadratfreie Zahlen, Math. Ann. 105 (1931), 653-662.
  • [7] D. R. Heath-Brown, On the fractional part of $αn^k$, Mathematika 35 (1988), 28-37.
  • [8] H. Z. Li, Waring's problem for sixteenth powers, Sci. China Ser. A 39 (1996), 56-64.
  • [9] Z. Z. Meng, Some new results in Waring's problem, Adv. in Math. (China) 25 (1996), 347-353.
  • [10] Z. Z. Meng, Some new results in Waring's problem, Acta Math. Sinica 12 (1996), 262-267.
  • [11] Z. Z. Meng, Some new results on Waring's problem, J. China Univ. Sci. Tech. 27 (1997), 1-5.
  • [12] R. C. Vaughan, On Waring's problem for smaller exponents, Proc. London Math. Soc. (3) 52 (1986), 445-463.
  • [13] R. C. Vaughan, A new iterative method in Waring's problem, Acta Math. 162 (1989), 1-71.
  • [14] R. C. Vaughan, A new iterative method in Waring's problem, II, J. London Math. Soc. (2) 39 (1989), 219-230.
  • [15] R. C. Vaughan, The Hardy-Littlewood Method, 2nd ed., Cambridge Univ. Press, Cambridge, 1997.
  • [16] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's problem, III: Eighth powers, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 385-396.
  • [17] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's problem, II: Sixth powers, Duke Math. J. 76 (1994), 683-710.
  • [18] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's problem, Acta Math. 174 (1995), 147-240.
  • [19] T. D. Wooley, Large improvements in Waring's problem, Ann. of Math. 135 (1992), 131-164.
  • [20] T. D. Wooley, The application of a new mean value theorem to the fractional parts of polynomials, Acta Arith. 65 (1993), 163-179.
  • [21] T. D. Wooley, Breaking classical convexity in Waring's problem: sums of cubes and quasi-diagonal behaviour, Invent. Math. 122 (1995), 421-451.
  • [22] T. D. Wooley, New estimates for smooth Weyl sums, J. London Math. Soc. (2) 51 (1995), 1-13.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav94i3p203bwm
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