On the Problem of Explicit Evaluation of the Number of Solutions of the Equation a1x 1 2 + ⋯ + a n x n 2 = bx1 ⋯ x n in a Finite Field
Ioulia N. Baoulina · Hindustan Book Agency · 2002
Let p be an odd rational prime, q = p s, s ≥ 1, and F q be the finite field of q elements. Let ε denote the trivial multiplicative character on F * and η denote the quadratic character on F * . The trivial character η is extended to all of F q by setting η(0) = 1. If ψ is a nontrivial character on F * we define ψ(0) = 0.