Abstract
When k≥k0=10 Mr2n log (rn) we have for the trigonometric integral
where
and E is the M-dimensional unit cube, the asymptotic formula
where σ is a singular series and θ is a singular integral.
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Translated from Matematicheskie Zametki, Vol. 23, No. 6, pp. 799–816, June, 1978.
The author would like to thank A. A. Karatsuba for his guidance and G. I. Arkhipov for his useful advice.
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Chubarikov, V.N. Asymptotic formula for the mean value of a multiple trigonometric sum. Mathematical Notes of the Academy of Sciences of the USSR 23, 438–448 (1978). https://doi.org/10.1007/BF01431424
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DOI: https://doi.org/10.1007/BF01431424