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September 2016 Small fractional parts of polynomials
Roger Baker
Funct. Approx. Comment. Math. 55(1): 131-137 (September 2016). DOI: 10.7169/facm/2016.55.1.9

Abstract

Let $k \ge 6$. Using the recent result of Bourgain, Demeter, and Guth \cite{1586:bdg} on the Vinogradov mean value, we obtain new bounds for small fractional parts of polynomials $\alpha_kn^k + \cdots + \alpha_1n$ and additive forms $\beta_1n_1^k + \cdots + \beta_sn_s^k$. Our results improve earlier theorems of Danicic (1957), Cook (1972), Baker (1982, 2000), Vaughan and Wooley (2000), and Wooley (2013).

Citation

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Roger Baker. "Small fractional parts of polynomials." Funct. Approx. Comment. Math. 55 (1) 131 - 137, September 2016. https://doi.org/10.7169/facm/2016.55.1.9

Information

Published: September 2016
First available in Project Euclid: 19 September 2016

zbMATH: 06862557
MathSciNet: MR3549017
Digital Object Identifier: 10.7169/facm/2016.55.1.9

Subjects:
Primary: 11J54

Rights: Copyright © 2016 Adam Mickiewicz University

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Vol.55 • No. 1 • September 2016
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