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Estimate of a complete rational trigonometric sum |
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| Authors: | V I Nechaev |
| Institution: | 1. V. A. Steklov Mathematical Institute, Academy of Sciences of the USSR, USSR |
| Abstract: | Supposef is a polynomial of degree n≥3 with integral coefficientsa 0,a 1,...,a n; q is a natural number; (a 1,...,a n, q)=1,f(0) = 0. It is proved that $$\left| {\sum\nolimits_{x = 1}^q {e^{2\pi if(x)/q} } } \right|< e^{5n^2 /\ln n} q^{1 - 1/n} $$ . |
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