This article is cited in 7 papers

Estimate of a complete rational trigonometric su

V. I. Nechaev

V. A. Steklov Mathematical Institute, Academy of Sciences of the USSR,

Abstract: Supposef is a polynomial of degree $n\ge3$ with integral coefficientsa $a_0,a_1,\dots,a_n$; $q$ is a natural number; ($a_1,\dots,a_n, q)=1$ $f(0)=0$. It is proved that
$$ \Bigl|\sum_{x=1}^qe^{2\pi if(x)/q}\Bigr|<e^{5n^2/\ln n}q^{1-1/n}. $$


UDC: 511

Received: 03.12.1974

 English version: Mathematical Notes, 1975, 17:6, 504–511

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