Matematičeskie zametki, Tome 20 (1976) no. 6, pp. 815-824
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G. I. Perel'muter. Estimate of a multidimensional sum with the Legendre symbol for a polynomial of odd degree. Matematičeskie zametki, Tome 20 (1976) no. 6, pp. 815-824. http://geodesic.mathdoc.fr/item/MZM_1976_20_6_a2/
@article{MZM_1976_20_6_a2,
author = {G. I. Perel'muter},
title = {Estimate of a~multidimensional sum with the {Legendre} symbol for a~polynomial of odd degree},
journal = {Matemati\v{c}eskie zametki},
pages = {815--824},
year = {1976},
volume = {20},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_6_a2/}
}
TY - JOUR
AU - G. I. Perel'muter
TI - Estimate of a multidimensional sum with the Legendre symbol for a polynomial of odd degree
JO - Matematičeskie zametki
PY - 1976
SP - 815
EP - 824
VL - 20
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_1976_20_6_a2/
LA - ru
ID - MZM_1976_20_6_a2
ER -
%0 Journal Article
%A G. I. Perel'muter
%T Estimate of a multidimensional sum with the Legendre symbol for a polynomial of odd degree
%J Matematičeskie zametki
%D 1976
%P 815-824
%V 20
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1976_20_6_a2/
%G ru
%F MZM_1976_20_6_a2
The estimate $$ \Bigl|\sum_{x,1\dots,x_n\in F_q}\chi(f(x_1,\dots,x_n))\Bigr|\le(d-1)^nq^{n/2}. $$ is derived for the quadratic character Lambda of a field $F_q$ of $q$ elements and a polynomial $f$ of odd degree $d$ over $F_q$ under certain natural conditions.
