Geodesic
Estimation of a~sum along an~algebraic curve
Matematičeskie zametki, Tome 5 (1969) no. 3, pp. 373-380.

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

Let $\Gamma$ be an algebraic curve determined over a finite field $k=[q]$; $e$, $\chi$ are subsidiary additive and multiplicative characters of the field $k$; $\varphi$, $\psi$ are functions in $\Gamma$ determined over $k$ and satisfying some natural conditions. If $P$ passes through the points of curve $\Gamma$, rational over $k$, then $$ \biggl|\sum_{P\in\Gamma}e(\varphi(P))\chi(\psi(P))\biggr|\leqslant C\sqrt q $$ where constant $C$ depends only on the powers of $\Gamma,\varphi,\psi$. 
@article{MZM_1969_5_3_a11,
     author = {G. I. Perel'muter},
     title = {Estimation of a~sum along an~algebraic curve},
     journal = {Matemati\v{c}eskie zametki},
     pages = {373--380},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_3_a11/}
}
TY  - JOUR
AU  - G. I. Perel'muter
TI  - Estimation of a~sum along an~algebraic curve
JO  - Matematičeskie zametki
PY  - 1969
SP  - 373
EP  - 380
VL  - 5
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1969_5_3_a11/
LA  - ru
ID  - MZM_1969_5_3_a11
ER  - 
%0 Journal Article
%A G. I. Perel'muter
%T Estimation of a~sum along an~algebraic curve
%J Matematičeskie zametki
%D 1969
%P 373-380
%V 5
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1969_5_3_a11/
%G ru
%F MZM_1969_5_3_a11
G. I. Perel'muter. Estimation of a~sum along an~algebraic curve. Matematičeskie zametki, Tome 5 (1969) no. 3, pp. 373-380. http://geodesic.mathdoc.fr/item/MZM_1969_5_3_a11/