Geodesic
Estimate of a~multiple sum involving the Legendre symbol
Matematičeskie zametki, Tome 18 (1975) no. 3, pp. 421-427

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Suppose $f(x_1,\dots,x_n)$ is a polynomial of even degree $d$ having coefficients in the finite field $k=[q]$ and satisfying certain natural conditions, and let $\chi$ be the quadratic character of $k$. Then $$ \Bigl|\sum x_1,\dots,x_n\in kx(f(x_1,\dots,x_n))\Bigr|\le Cq^{n/2}, $$ where the constant $C$ depends only on $d$ and $n$. 
@article{MZM_1975_18_3_a10,
     author = {G. I. Perel'muter},
     title = {Estimate of a~multiple sum involving the {Legendre} symbol},
     journal = {Matemati\v{c}eskie zametki},
     pages = {421--427},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_3_a10/}
}
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G. I. Perel'muter. Estimate of a~multiple sum involving the Legendre symbol. Matematičeskie zametki, Tome 18 (1975) no. 3, pp. 421-427. http://geodesic.mathdoc.fr/item/MZM_1975_18_3_a10/