Abstract:
We prove estimates for complete rational arithmetic sums of Bernoulli polynomials whose arguments are formed by the fractional parts of values of a polynomial with rational coefficients. The results are applied to the problem of finding the convergence exponent for the mean values of the sums under consideration.
Citation:
V. N. Chubarikov, “On an elementary version of I.M. Vinogradov's method”, Analytic and combinatorial number theory, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 296, MAIK Nauka/Interperiodica, Moscow, 2017, 47–57; Proc. Steklov Inst. Math., 296 (2017), 41–51
\Bibitem{Chu17}
\by V.~N.~Chubarikov
\paper On an elementary version of I.M. Vinogradov's method
\inbook Analytic and combinatorial number theory
\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov
\serial Trudy Mat. Inst. Steklova
\yr 2017
\vol 296
\pages 47--57
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3790}
\crossref{https://doi.org/10.1134/S0371968517010046}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2017
\vol 296
\pages 41--51
\crossref{https://doi.org/10.1134/S0081543817010047}
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Linking options:
https://www.mathnet.ru/eng/tm3790
https://doi.org/10.1134/S0371968517010046
https://www.mathnet.ru/eng/tm/v296/p47
This publication is cited in the following 1 articles:
V. N. Chubarikov, “Multiple complete rational arithmetic sums of polynomial values”, Dokl. Math., 97:1 (2018), 15–17
Citation in format AMSBIB
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