Abstract
A two-dimensional analog of the Vinogradov mean-value theorem for the modulus of trigonometric sums is proven.
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I. M. Vinogradov, Method of Trigonometric Sums in Number Theory [in Russian], Moscow (1971).
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Translated from Matematicheskie Zametki, Vol. 17, No. 1, pp. 143–153, January, 1975.
The author expresses his gratitude fo Prof. A. A. Karatsuba for guidance and Prof. S. B. Stechkin for careful consideration of the paper and useful advice.
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Arkhipov, G.I. Mean-value theorem for the modulus of multiple trigonometric sums. Mathematical Notes of the Academy of Sciences of the USSR 17, 84–90 (1975). https://doi.org/10.1007/BF01093850
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DOI: https://doi.org/10.1007/BF01093850