# Limitation to the asymptotic formula in Waring's problem

Acta Arithmetica (1996)

- Volume: 74, Issue: 1, page 1-15
- ISSN: 0065-1036

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topW. K. A. Loh. "Limitation to the asymptotic formula in Waring's problem." Acta Arithmetica 74.1 (1996): 1-15. <http://eudml.org/doc/206834>.

@article{W1996,

author = {W. K. A. Loh},

journal = {Acta Arithmetica},

keywords = {Waring's problem; error term; asymptotic formula; number of representations; asymptotic value; circle method},

language = {eng},

number = {1},

pages = {1-15},

title = {Limitation to the asymptotic formula in Waring's problem},

url = {http://eudml.org/doc/206834},

volume = {74},

year = {1996},

}

TY - JOUR

AU - W. K. A. Loh

TI - Limitation to the asymptotic formula in Waring's problem

JO - Acta Arithmetica

PY - 1996

VL - 74

IS - 1

SP - 1

EP - 15

LA - eng

KW - Waring's problem; error term; asymptotic formula; number of representations; asymptotic value; circle method

UR - http://eudml.org/doc/206834

ER -

## References

top- [1] K. D. Boklan, The asymptotic formula in Waring's Problem, Mathematika 41 (1994), 329-347. Zbl0815.11050
- [2] G. H. Hardy, On the representation of a number as the sum of any number of squares, and in particular of five, Trans. Amer. Math. Soc. 21 (1920), 255-284. Zbl47.0883.03
- [3] G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio Numerorum', IV, Math. Z. 12 (1922), 161-188. Zbl48.0146.01
- [4] D. R. Heath-Brown, Weyl's inequality, Hua's inequality, and Waring's problem, J. London Math. Soc. 38 (1988), 216-230. Zbl0619.10046
- [5] L. K. Hua, On Waring's problem, Quart. J. Math. Oxford 9 (1938), 199-202. Zbl64.0124.04
- [6] L. K. Hua, An improvement of Vinogradov's mean-value theorem and several applications, Quart. J. Math. Oxford 20 (1949), 48-61. Zbl0039.27403
- [7] H. L. Montgomery and R. C. Vaughan, Error terms in additive prime number theory, Quart. J. Math. Oxford 24 (1973), 207-216. Zbl0257.10027
- [8] R. C. Vaughan, On the addition of sequences of integers, J. Number Theory 4 (1972), 1-16. Zbl0226.10058
- [9] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge University Press, 1981. Zbl0455.10034
- [10] R. C. Vaughan, On Waring's problem for cubes, J. Reine Angew. Math. 365 (1986), 122-170. Zbl0574.10046
- [11] R. C. Vaughan, On Waring's problem for smaller exponent II, Mathematika 33 (1986), 6-22. Zbl0601.10037
- [12] I. M. Vinogradov, New estimates for Weyl's sum, Dokl. Akad. Nauk SSSR 8 (1935), 195-198.
- [13] T. D. Wooley, On Vinogradov's mean value theorem, Mathematika 39 (1992), 379-399. Zbl0769.11036

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