Geodesic
On the Number of Zeros Over a Finite Field of Certain Symmetric Polynomials
Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 327-332

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A variety of applications depend on the number of solutions of polynomial equations over finite fields. Here the usual situation is reversed and we show how to use geometrical methods to estimate the number of solutions of a non-homogeneous symmetric equation in three variables. 
Ceccherini, P. V.; Hirschfeld, J. W. P. On the Number of Zeros Over a Finite Field of Certain Symmetric Polynomials. Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 327-332. doi: 10.4153/CMB-1980-046-5
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     author = {Ceccherini, P. V. and Hirschfeld, J. W. P.},
     title = {On the {Number} of {Zeros} {Over} a {Finite} {Field} of {Certain} {Symmetric} {Polynomials}},
     journal = {Canadian mathematical bulletin},
     pages = {327--332},
     year = {1980},
     volume = {23},
     number = {3},
     doi = {10.4153/CMB-1980-046-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-046-5/}
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