Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 839-849
Citer cet article
V. I. Nechaev. Estimate of a complete rational trigonometric su. Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 839-849. http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a1/
@article{MZM_1975_17_6_a1,
author = {V. I. Nechaev},
title = {Estimate of a ~complete rational trigonometric su},
journal = {Matemati\v{c}eskie zametki},
pages = {839--849},
year = {1975},
volume = {17},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a1/}
}
TY - JOUR
AU - V. I. Nechaev
TI - Estimate of a complete rational trigonometric su
JO - Matematičeskie zametki
PY - 1975
SP - 839
EP - 849
VL - 17
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a1/
LA - ru
ID - MZM_1975_17_6_a1
ER -
%0 Journal Article
%A V. I. Nechaev
%T Estimate of a complete rational trigonometric su
%J Matematičeskie zametki
%D 1975
%P 839-849
%V 17
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a1/
%G ru
%F MZM_1975_17_6_a1
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}. $$
