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On Hua's estimates for exponential sums

Published online by Cambridge University Press:  26 February 2010

J. H. H. Chalk
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ont. M5S 1A1, Canada.
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Extract

Let

and let p denote any prime. The p-content vp(f) of f is denned by

Type
Research Article
Copyright
Copyright © University College London 1987

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References

1.Carlitz, L. and Uchiyama, S.. Bounds for Exponential Sums. Duke Math. Jour., 24 (1975), 3741.Google Scholar
2.Chalk, J. H. H.. On Incomplete Character Sums to a prime-power modulus. Canad. Math. Bull., 30 (3) (1987), 257266.CrossRefGoogle Scholar
3.Hua, Loo-Keng. “Additiv Primzahltheorie” (Teubner, Leipzig, 1959), Ch. 1, 27.Google Scholar
4.Hua, Loo-Keng. Die Abschätzung von Exponentialsummen und ihre Anwendung in der Zahlentheorie (1959) Enzyklopädie der Math. Wiss., Bd I2, H.13, TI section 13, S41.Google Scholar
5.Loxton, J. H. and Smith, R. A.. On Hua's Estimate for Exponential Sums. Jour. London Math. Soc., (2), 26 (1982), 1520.CrossRefGoogle Scholar
6.Loxton, J. H. and Vaughan, R. C.. The Estimation of Complete Exponential Sums. Canad. Math. Bull., 28 (1985), 440454.CrossRefGoogle Scholar
7.Weil, A.. On some exponential sums. Proc. Nat. Acad. Sci., U.S.A., 34 (1948), 204207.CrossRefGoogle ScholarPubMed