Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2016, Number 1, Pages 60–61 (Mi vmumm125)  
This article is cited in 5 scientific papers (total in 5 papers)

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Complete rational arithmetic sums

V. N. Chubarikov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (296 kB) Citations (5)
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Abstract: Let $q>1$ be an integer, $f(x)=a_nx^n+\ldots +a_1x+a_0$ be a polynomial with the integer coefficients, and $(a_n,\ldots ,a_1,q)=1.$ Then is valid the estimation
$$\left|S\left(\frac{f(x)}{q}\right)\right|=\left|\sum_{x=1}^q\rho\left(\frac{f(x)}q\right)\right|\ll q^{1-1/n}, $$
where $\rho(t)=0,5-\{t\}.$
Key words: “the saw-tooth” function, the Bernuolli's polynomials, the complete rational arithmetical sums.
Received: 27.03.2015
English version:
Moscow University Mathematics Bulletin, 2016, Volume 71, Issue 1, Pages 43–44
DOI: https://doi.org/10.3103/S0027132216010095
Bibliographic databases:
Document Type: Article
UDC: 511
Language: Russian
Citation: V. N. Chubarikov, “Complete rational arithmetic sums”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 1, 60–61; Moscow University Mathematics Bulletin, 71:1 (2016), 43–44
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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