Geodesic
On the Number and Distribution of Simultaneous Solutions to Diagonal Congruences
Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 421-436

Voir la notice de l'article provenant de la source Cambridge University Press

Two aspects, and their connections, of the problem of enumerating solutions to certain systems of congruences are explored in this paper. Although slightly more general cases are mentioned, the basic object of study is a system of diagonal equations where d 1, d 2, ..., dt are positive integers and the coefficient matrix [aij] has entries from Fp = GF(p), and for which solutions x = (x 1, x 2 ..., xt ) ∈ Fpt are sought. Speaking loosely, such a system usually has approximately p t–n solutions in the sense that the difference between pt–n and the correct value becomes small in comparison with pt–n as p becomes large. A parameter is introduced which measures the extent to which the matrix [aij] is non-singular over Fp. The effect of this parameter on the size of the error term (the difference between the number of solutions to (1) and pt–n ) is the first aspect of the enumeration problem to be treated. 
Spackman, Kenneth W. On the Number and Distribution of Simultaneous Solutions to Diagonal Congruences. Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 421-436. doi: 10.4153/CJM-1981-037-x
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