The application of a new mean value theorem to the fractional parts of polynomials

Trevor D. Wooley

Acta Arithmetica (1993)

  • Volume: 65, Issue: 2, page 163-179
  • ISSN: 0065-1036

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Trevor D. Wooley. "The application of a new mean value theorem to the fractional parts of polynomials." Acta Arithmetica 65.2 (1993): 163-179. <http://eudml.org/doc/206568>.

@article{TrevorD1993,
author = {Trevor D. Wooley},
journal = {Acta Arithmetica},
keywords = {mean value estimates; Waring problems; fractional parts of monomials},
language = {eng},
number = {2},
pages = {163-179},
title = {The application of a new mean value theorem to the fractional parts of polynomials},
url = {http://eudml.org/doc/206568},
volume = {65},
year = {1993},
}

TY - JOUR
AU - Trevor D. Wooley
TI - The application of a new mean value theorem to the fractional parts of polynomials
JO - Acta Arithmetica
PY - 1993
VL - 65
IS - 2
SP - 163
EP - 179
LA - eng
KW - mean value estimates; Waring problems; fractional parts of monomials
UR - http://eudml.org/doc/206568
ER -

References

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  1. [1] R. C. Baker, Diophantine Inequalities, London Math. Soc. Monographs (N.S.) 1, Clarendon Press, Oxford, 1986. 
  2. [2] R. C. Baker, J. Brüdern and G. Harman, The fractional part of α n k for square-free n, Quart. J. Math. Oxford (2) 42 (1991), 421-431. Zbl0751.11038
  3. [3] I. Danicic, Contributions to Number Theory, Ph.D. Thesis, London, 1957. 
  4. [4] G. Harman, Trigonometric sums over primes I, Mathematika 28 (1981), 249-254. Zbl0465.10029
  5. [5] D. R. Heath-Brown, On the fractional part of α n k , Mathematika 35 (1988), 28-37. Zbl0629.10029
  6. [6] H. Heilbronn, On the distribution of the sequence n²θ (mod 1), Quart. J. Math. Oxford 19 (1948), 249-256. Zbl0031.20502
  7. [7] K. Thanigasalam, Some new estimates for G(k) in Waring's problem, Acta Arith. 42 (1982), 73-78. Zbl0496.10030
  8. [8] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Tracts Math. 80, Cambridge Univ. Press, 1981. 
  9. [9] R. C. Vaughan, A new iterative method in Waring's problem, Acta Math. 162 (1989), 1-71. Zbl0665.10033
  10. [10] R. C. Vaughan, A new iterative method in Waring's problem, II, J. London Math. Soc. (2) 39 (1989), 219-230. Zbl0677.10035
  11. [11] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's problem, to appear. Zbl0849.11075
  12. [12] I. M. Vinogradov, Analytischer Beweis des Satzes über die Verteilung der Bruch- teile eines ganzen Polynoms, Bull. Acad. Sci. USSR (6) 21 (1927), 567-578. Zbl53.0160.02
  13. [13] H. Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352. Zbl46.0278.06
  14. [14] T. D. Wooley, Large improvements in Waring's problem, Ann. of Math. 135 (1992), 131-164. Zbl0754.11026

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