Estimates of character sums with exponential function
نویسندگان
چکیده
منابع مشابه
Estimates for Mixed Character Sums
a nontrivial additive character of k. We are given a polynomial f = f(x1, ..., xn) in n ≥ 1 variables over k of degree d ≥ 1 which is a “Deligne polynomial”, i.e., its degree d is prime to p and its highest degree term, say fd, is a homogeneous form of degree d in n variables which is nonzero, and whose vanishing, if n ≥ 2, defines a smooth hypersurface in the projective space Pn−1. For a Delig...
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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 necess...
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a nontrivial multiplicative character of k. We extend χ to k by defining χ(0) = 0. We wish to consider character sums over An, n ≥ 1, of the following form. We are given a polynomial f (x) := f (x1, . . . , xn) in k[x1, . . . ,Xn] of degree d ≥ 1, and we are given a second polynomial g(X) := g(x1, . . . , xn) in k[x1, . . . , xn] of degree e ≥ 1. We are interested in understanding when the sum ...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2001
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa97-3-2