Abstract:
The author obtains estimates for multiple trigonometric sums with a general polynomial in the exponent whose variables of summation take the values of the successive prime numbers. The precision of the estimates is similar to that of the estimates in the paper "Multiple trigonometric sums and their applications" by Arkhipov, Karatsuba and Chubarikov (Izv. Akad. Nauk SSSR Ser. Mat., 1980, v. 44, № 4, p. 723–781).
Bibliography: 12 titles.
\Bibitem{Chu85}
\by V.~N.~Chubarikov
\paper Estimates of multiple trigonometric sums with prime numbers
\jour Math. USSR-Izv.
\yr 1986
\vol 27
\issue 2
\pages 323--357
\mathnet{http://mi.mathnet.ru/eng/im1376}
\crossref{https://doi.org/10.1070/IM1986v027n02ABEH001180}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=810529}
\zmath{https://zbmath.org/?q=an:0608.10037|0599.10031}
Linking options:
https://www.mathnet.ru/eng/im1376
https://doi.org/10.1070/IM1986v027n02ABEH001180
https://www.mathnet.ru/eng/im/v49/i5/p1031
This publication is cited in the following 9 articles:
V. N. Chubarikov, “Mean-Value Theorem for Multiple Trigonometric Sums on the Sequence of Bell Polynomials”, Proc. Steklov Inst. Math., 314 (2021), 290–299
Kh. M. Saliba, V. N. Chubarikov, “O nekotorykh additivnykh problemakh goldbakhova tipa”, Chebyshevskii sb., 22:3 (2021), 179–195
V. N. Chubarikov, “Teorema o srednem znachenii trigonometricheskikh summ na posledovatelnosti mnogochlenov binomialnogo tipa”, Chebyshevskii sb., 21:2 (2020), 403–416
V. N. Chubarikov, “Ob odnoi teoreme o srednem znachenii kratnykh trigonometricheskikh summ”, Chebyshevskii sb., 21:1 (2020), 341–356
V. N. Chubarikov, “On multiple trigonometric sums related with prime numbers”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 75:6 (2020), 227–238
V. N. Chubarikov, “Obobschennaya formula binoma Nyutona i formuly summirovaniya”, Chebyshevskii sb., 21:4 (2020), 270–301
M. P. Mineev, V. N. Chubarikov, “I.M. Vinogradov's method in number theory and its current development”, Proc. Steklov Inst. Math., 296 (2017), 1–17
I. P. Mikhailov, “On multiple trigonometric sums of mixed type”, Discrete Math. Appl., 22:1 (2012), 41–44
V. N. Chubarikov, “Mnogomernye problemy teorii prostykh chisel”, Chebyshevskii sb., 12:4 (2011), 174–263
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