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

R. Vaughan; T. Wooley

Acta Arithmetica (2000)

  • Volume: 94, Issue: 3, page 203-285
  • ISSN: 0065-1036

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Vaughan, R., and Wooley, T.. "Further improvements in Waring's problem, IV: Higher powers." Acta Arithmetica 94.3 (2000): 203-285. <http://eudml.org/doc/207431>.

@article{Vaughan2000,
author = {Vaughan, R., Wooley, T.},
journal = {Acta Arithmetica},
keywords = {Waring's problem; efficient differencing; Hardy-Littlewood method},
language = {eng},
number = {3},
pages = {203-285},
title = {Further improvements in Waring's problem, IV: Higher powers},
url = {http://eudml.org/doc/207431},
volume = {94},
year = {2000},
}

TY - JOUR
AU - Vaughan, R.
AU - Wooley, T.
TI - Further improvements in Waring's problem, IV: Higher powers
JO - Acta Arithmetica
PY - 2000
VL - 94
IS - 3
SP - 203
EP - 285
LA - eng
KW - Waring's problem; efficient differencing; Hardy-Littlewood method
UR - http://eudml.org/doc/207431
ER -

References

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  2. [2] E. Bombieri and J. Pila, The number of integral points on arcs and ovals, Duke Math. J. 59 (1989), 337-357. Zbl0718.11048
  3. [3] J. Brüdern, A problem in additive number theory, Math. Proc. Cambridge Philos. Soc. 103 (1988), 27-33. Zbl0655.10041
  4. [4] J. Brüdern and T. D. Wooley, On Waring's problem for cubes and smooth Weyl sums, Proc. London Math. Soc., to appear. Zbl1016.11044
  5. [5] I. Danicic, Contributions to Number Theory, Ph.D. thesis, London, 1957. 
  6. [6] T. Estermann, Einige Sätze über quadratfreie Zahlen, Math. Ann. 105 (1931), 653-662. Zbl57.0222.02
  7. [7] D. R. Heath-Brown, On the fractional part of α n k , Mathematika 35 (1988), 28-37. Zbl0629.10029
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  12. [12] R. C. Vaughan, On Waring's problem for smaller exponents, Proc. London Math. Soc. (3) 52 (1986), 445-463. Zbl0601.10035
  13. [13] R. C. Vaughan, A new iterative method in Waring's problem, Acta Math. 162 (1989), 1-71. Zbl0665.10033
  14. [14] R. C. Vaughan, A new iterative method in Waring's problem, II, J. London Math. Soc. (2) 39 (1989), 219-230. Zbl0677.10035
  15. [15] R. C. Vaughan, The Hardy-Littlewood Method, 2nd ed., Cambridge Univ. Press, Cambridge, 1997. Zbl0868.11046
  16. [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. Zbl0849.11077
  17. [17] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's problem, II: Sixth powers, Duke Math. J. 76 (1994), 683-710. Zbl0849.11076
  18. [18] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's problem, Acta Math. 174 (1995), 147-240. Zbl0849.11075
  19. [19] T. D. Wooley, Large improvements in Waring's problem, Ann. of Math. 135 (1992), 131-164. Zbl0754.11026
  20. [20] T. D. Wooley, The application of a new mean value theorem to the fractional parts of polynomials, Acta Arith. 65 (1993), 163-179. Zbl0789.11037
  21. [21] T. D. Wooley, Breaking classical convexity in Waring's problem: sums of cubes and quasi-diagonal behaviour, Invent. Math. 122 (1995), 421-451. Zbl0851.11055
  22. [22] T. D. Wooley, New estimates for smooth Weyl sums, J. London Math. Soc. (2) 51 (1995), 1-13. Zbl0833.11041

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