The Newton Polygon of Gauss-Heilbronn Sums
نویسنده
چکیده
Let p be a prime, Zp the ring of p-adic integers, Qp the field of p-adic numbers, and Qp the algebraic closure of Qp. Let Fp be the algebraic closure of the finite field Fp, and ω : Fp → Qp the Techmüller lifting. Let q = pa, χ a multiplicative character of Fq into Q, and ψ a character of Zp[μq−1] into Q of exact order pn > 1, where μr is the set of r-th roots of unity in Qp. For simplicity, we assume that ψ = ψ0 ◦ TrQp(μq−1)/Qp , where ψ0 is a character of Zp into Q of exact order pn. We are concerned with the exponential sum S(χ,ψ) := ∑
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