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A generalization of the Gauss sum

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Moscow University Mathematics Bulletin Aims and scope

Abstract

For the generalized Gauss sum

$$ S(N;a,q) = \sum\limits_{k = 1}^{Nq} e \left( {\frac{1} {N}\left( {k - \frac{a} {q}} \right)^2 } \right) $$

, where N, q are natural numbers, a is integer, 0 ≤ a < q, (a, q) = 1, its value is determined.

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References

  1. G. I. Arkhipov, V. A. Sadovnichii, and V. N. Chubarikov, Lectures in Mathematical Analysis, 5th ed. (Drofa, Moscow, 2004) [in Russian].

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  2. I. M. Vinogradov, Foundations of the Theory of Numbers, (Nauka, Moscow, 1983; 6th ed. Pergamon Press, New York, 1955).

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    Kh. M. Saliba & V. N. Chubarikov

Authors
  1. Kh. M. Saliba
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  2. V. N. Chubarikov
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Additional information

Original Russian Text © Kh.M. Saliba, V.N. Chubarikov, 2009, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2009, Vol. 64, No. 2, pp. 77–80.

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Saliba, K.M., Chubarikov, V.N. A generalization of the Gauss sum. Moscow Univ. Math. Bull. 64, 92–94 (2009). https://doi.org/10.3103/S0027132209020132

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  • DOI: https://doi.org/10.3103/S0027132209020132

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