On Waring's problem with polynomial summands

Hong Bing Yu

Acta Arithmetica (1996)

  • Volume: 76, Issue: 2, page 131-144
  • ISSN: 0065-1036

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Hong Bing Yu. "On Waring's problem with polynomial summands." Acta Arithmetica 76.2 (1996): 131-144. <http://eudml.org/doc/206890>.

@article{HongBingYu1996,
author = {Hong Bing Yu},
journal = {Acta Arithmetica},
keywords = {integral-valued polynomial; singular series; Waring's problem with polynomial summands},
language = {eng},
number = {2},
pages = {131-144},
title = {On Waring's problem with polynomial summands},
url = {http://eudml.org/doc/206890},
volume = {76},
year = {1996},
}

TY - JOUR
AU - Hong Bing Yu
TI - On Waring's problem with polynomial summands
JO - Acta Arithmetica
PY - 1996
VL - 76
IS - 2
SP - 131
EP - 144
LA - eng
KW - integral-valued polynomial; singular series; Waring's problem with polynomial summands
UR - http://eudml.org/doc/206890
ER -

References

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  1. [1] K. D. Boklan, The asymptotic formula in Waring's problem, Mathematika 41 (1994), 329-347. Zbl0815.11050
  2. [2] H. Davenport, On Waring's problem for cubes, Acta Math. 71 (1939), 123-143. Zbl0021.10601
  3. [3] H. Davenport, On sums of positive integral k-th powers, Amer. J. Math. 64 (1942), 189-198. Zbl0060.11908
  4. [4] D. R. Heath-Brown, Weyl's inequality, Hua's inequality, and the Waring's problem, J. London Math. Soc. (2) 38 (1988), 216-230. Zbl0619.10046
  5. [5] L. K. Hua, On Waring's problem with polynomial summands, Amer. J. Math. 58 (1936), 553-562. Zbl62.0148.02
  6. [6] L. K. Hua, On a generalized Waring problem, Proc. London Math. Soc. (2) 43 (1937), 161-182. Zbl63.0127.02
  7. [7] L. K. Hua, Some results on Waring's problem for smaller powers, C. R. Acad. Sci. URSS (2) 18 (1938), 527-528. Zbl64.0124.03
  8. [8] L. K. Hua, On a generalized Waring problem, II, J. Chin. Math. Soc. 2 (1940), 175-191. Zbl0061.07404
  9. [9] L. K. Hua, On a Waring's problem with cubic polynomial summands, J. Indian Math. Soc. 4 (1940), 127-135. 
  10. [10] L. K. Hua, Die Abschätzung von Exponentialsummen und ihre anwendung in der Zahlentheorie, Enzyklopädie der Math. Wiss. Band I,2. Heft 13, Teil 1, Teubner, Leipzig, 1959. 
  11. [11] V. I. Nechaev, Waring's problem for polynomials, Trudy Mat. Inst. Steklov 38 (1951), 190-243. Zbl0053.35904
  12. [12] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Univ. Press, 1981. Zbl0455.10034
  13. [13] R. C. Vaughan, On Waring's problem for cubes, J. Reine Angew. Math. 365 (1986), 122-170. Zbl0574.10046
  14. [14] R. C. Vaughan, On Waring's problem for smaller exponents, Proc. London Math. Soc. (3) 52 (1986), 445-463. Zbl0601.10035
  15. [15] R. C. Vaughan, On Waring's problem for smaller exponents, II, Mathematika 33 (1986), 6-22. Zbl0601.10037
  16. [16] R. C. Vaughan, A new iterative method in Waring's problem, Acta Math. 162 (1989), 1-70. Zbl0665.10033
  17. [17] R. C. Vaughan, The use in additive number theory of numbers without large prime factors, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 363-376. Zbl0849.11074
  18. [18] R. C. Vaughan and T. D. Wooley, On Waring's problem: some refinements, Proc. London Math. Soc. 63 (1991), 35-68. Zbl0736.11058

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