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Mean-value theorem of I. M. Vinogradov for a trigonometric sum over Gaussian numbers

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Abstract

A mean-value theorem for the absolute value of trigonometric sums in the ring of Gaussian numbers is proved.

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References

  1. I. M. Kozlov, Additive Problems in Algebraic Fields, Candidate’s Dissertation in Mathematics and Physics (Moscow, 2002) [in Russian].

  2. G. I. Arkhipov, A. A. Karatsuba, and B. N. Chubarikov, Theory of Multiple Trigonometric Sums (Nauka, Moscow, 1987) [in Russian].

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  3. I. M. Vinogradov, The Method of Trigonometric Sums in Number Theory (Nauka, Moscow, 1980) [in Russian].

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  4. A. A. Karatsuba, Foundations of the Analytical Number Theory (Nauka, Moscow, 1975) [in Russian].

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  5. O. V. Tyrina, Mean Values of Trigonometric Sums, Candidate’s Dissertation in Mathematics and Physics (Moscow, 1989) [in Russian].

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Authors and Affiliations

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

    P. N. Sorokin

Authors
  1. P. N. Sorokin
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Additional information

Original Russian Text © P.N. Sorokin, 2007, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2007, Vol. 62, No. 6, pp. 63–65.

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Sorokin, P.N. Mean-value theorem of I. M. Vinogradov for a trigonometric sum over Gaussian numbers. Moscow Univ. Math. Bull. 62, 256–258 (2007). https://doi.org/10.3103/S0027132207060101

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  • DOI: https://doi.org/10.3103/S0027132207060101

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