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
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
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