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

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

$q>1$ be an integer,

f (x) = a_{n} x^{n} + \dots + a_{1} x + a_{0}

$f(x)=a_nx^n+\ldots +a_1x+a_0$ be a polynomial with the integer coefficients, and

(a_{n}, \dots, a_{1}, q) = 1.

$(a_n,\ldots ,a_1,q)=1.$ Then is valid the estimation

| S (\frac{f (x)}{q}) | = | \sum_{x = 1}^{q} ρ (\frac{f (x)}{q}) | ≪ q^{1 - 1 / n},

$\left|S\left(\frac{f(x)}{q}\right)\right|=\left|\sum_{x=1}^q\rho\left(\frac{f(x)}q\right)\right|\ll q^{1-1/n},$
where

ρ (t) = 0, 5 - {t} .

$\rho(t)=0,5-\{t\}.$

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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Linking options:

https://www.mathnet.ru/eng/vmumm125

https://www.mathnet.ru/eng/vmumm/y2016/i1/p60

This publication is cited in the following 5 articles:

Vladimir Nikolaevich Chubarikov, “Obobschennye summy Gaussa i mnogochleny Bernulli”, Chebyshevskii Sbornik, 20:1 (2019), 282
V. N. Chubarikov, “On an elementary version of I.M. Vinogradov's method”, Proc. Steklov Inst. Math., 296 (2017), 41–51
V. N. Chubarikov, “On complete rational arithmetic sums of polynomial values”, Proc. Steklov Inst. Math., 299 (2017), 50–55
V. N. Chubarikov, M. L. Sharapova, “A cubature formula for periodic functions”, Mosc. Univ. Math. Bull., 72:6 (2017), 255–257
V. N. Chubarikov, “Pokazatel skhodimosti srednego znacheniya polnykh ratsionalnykh arifmeticheskikh summ”, Chebyshevskii sb., 16:4 (2015), 303–318

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	56

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