Geodesic
Estimate of a~sum of Legendre symbols of polynomials of even degree
Matematičeskie zametki, Tome 14 (1973) no. 1, pp. 73-81.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $n\ge4$ be even, $p>\frac{n^2-2n}2$ be simple odd, and $f(x)=a_0+a_1x+\dots+a_nx^n$ be a polynomial with integral coefficients that are not quadratic over the residue field modulo $p$, $(a_n,p)=1$. The following inequality is proved: $$ \biggl|\sum_{x=1}^p\biggl(\frac{f(x)}p\biggr)\biggr|\le(n-2)\sqrt{p+1-\frac{n(n-4)}4}+1. $$ 
@article{MZM_1973_14_1_a9,
     author = {D. A. Mit'kin},
     title = {Estimate of a~sum of {Legendre} symbols of polynomials of even degree},
     journal = {Matemati\v{c}eskie zametki},
     pages = {73--81},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a9/}
}
TY  - JOUR
AU  - D. A. Mit'kin
TI  - Estimate of a~sum of Legendre symbols of polynomials of even degree
JO  - Matematičeskie zametki
PY  - 1973
SP  - 73
EP  - 81
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a9/
LA  - ru
ID  - MZM_1973_14_1_a9
ER  - 
%0 Journal Article
%A D. A. Mit'kin
%T Estimate of a~sum of Legendre symbols of polynomials of even degree
%J Matematičeskie zametki
%D 1973
%P 73-81
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a9/
%G ru
%F MZM_1973_14_1_a9
D. A. Mit'kin. Estimate of a~sum of Legendre symbols of polynomials of even degree. Matematičeskie zametki, Tome 14 (1973) no. 1, pp. 73-81. http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a9/