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Mean values of character sums

Published online by Cambridge University Press:  26 February 2010

D. A. Burgess
D. A. Burgess
Affiliation:
Mathematics Department, The University, Nottingham, England NG7 2RD.
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Extract

In 1979 Montgomery and Vaughan [3] showed that for each k > 0

the sum being over the non-principal characters χ modulo q. As a corollary they deduced that, if 0 < θ < 1 then there is a constant c(θ) such that at least θφ(q) of the non-principal characters χ modulo q satisfy

Type
Research Article
Information
Mathematika , Volume 33 , Issue 1 , June 1986 , pp. 1 - 5
Copyright
Copyright © University College London 1986

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References

1.Burgess, D. A.. On character sums and L-series II. Proc. London Math. Soc., (3), 13 (1963), 524–536.CrossRefGoogle Scholar
2.Davenport, H. and Erdős, P.. The distribution of quadratic and higher residues. Publ. Math. Debrecen, 2 (1952), 252–265.CrossRefGoogle Scholar
3.Montgomery, H. L. and Vaughan, R. C.. Mean values of character sums. Can. J. Math., 31 (1979), 476–487.CrossRefGoogle Scholar
4.Vinogradov, A. I.. On the symmetry property of sums with Dinchlet characters, Izv Akad Nauk Uz SSR. Ser. Fiz-Mat Nauk, (1965) 21–27.Google Scholar