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On incomplete Gaussian sums

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Abstract

In this paper it is proved that

$$\sum\limits_{N = N + 1}^{N + H} {x(n)\psi (n) \ll _\varepsilon H^{1 - \tfrac{1}{r}} q^{\tfrac{1}{{4(r - 1)}} + \varepsilon } } ,$$

wherer=4,q is a prime power,χ andψ are multiplicative and additive characters moduloq respectively, withχ nontrivial.

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References

  1. Burgess D A, Partial Gaussian sums II,Bull London Math Soc, 1989,21: 153–158.

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  2. Burgess D A, On a set of congruences related to character sums III,J London Math Soc, 1992,45: 201–214.

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Author notes

  1. Liu Chunlei

    Present address: Department of Mathematics, Sichuan University, 610064, Chengdu, China

Authors and Affiliations

  1. Department of Mathematics, Peking University, 100871, Beijing, China

    Liu Chunlei

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  1. Liu Chunlei
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Supported by the Natural Science Foundation of China.

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Chunlei, L. On incomplete Gaussian sums. Acta Mathematica Sinica 12, 141–150 (1996). https://doi.org/10.1007/BF02108155

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  • DOI: https://doi.org/10.1007/BF02108155

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