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System of inequalities

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Abstract

Let Nk,n,r(P) be a number of integer solutions of the system of inequalities

The main result is the following estimate for k − n2/4≫ nr log r

This estimate has the right order with respect to P. For r=n this is the classical Vinogradov mean value theorem.

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Literature cited

  1. I. M. Vinogradov, The Method of Trigonometric Sums in the Theory of Numbers, Wiley-Interscience, New York.

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Authors
  1. V. A. Bykovskii
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 109, pp. 3–33, 1981.

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Bykovskii, V.A. System of inequalities. J Math Sci 24, 159–178 (1984). https://doi.org/10.1007/BF01087239

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  • DOI: https://doi.org/10.1007/BF01087239

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