Estimates for \nonsingular" Multiplicative Character Sums
نویسنده
چکیده
Let k be a nite eld of characteristic p and cardinality q, a nontrivial C -valued additive character of k, and a nontrivial C -valued multiplicative character of k . We extend to a function on all of k by de ning (0) := 0: Recall that, given an integer n, a number 2 C is said to be pure of weight n (relative to q) if it and all its Aut(C =Q)-conjugates have absolute value p q. Such an is necessarily algebraic over Q. Fix a polynomial f(X) in k[X] of degree d 1. If d is prime to p, one has the estimate j X
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