On the coefficients of Jacobi sums in prime cyclotomic fields
نویسندگان
چکیده
منابع مشابه
Cyclotomic-intermediate Fields via Gauss Sums
Let p be an odd prime, and let m divide p−1. Let ζ = e and let ω = e. The field extension Q(ω) ⊂ Q(ω, ζ) is Galois with cyclic Galois group isomorphic to (Z/pZ)×. The unique field between Q(ω) and Q(ω, ζ) having degree m over Q(ω) takes the form Q(ω, τ) where τ is a Gauss sum, to be described below. Furthermore, under some conditions we can compute τ as an element α of Q(ω), thus expressing the...
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where χ, ψ is a non trivial character of Fq , whose value at 0 is defined to be 0. It is well known that the absolute value of J(χ, ψ) is √ q = p, when χψ is not principal. According to [11], [9], call the Jacobi sum J(χ, ψ) pure if J(χ, ψ)/p is a root of unity. Let ord(χ) be the order of χ in F̂×q . From now on in this paper, we assume that ord(ψ) = 2 and ord(χ) = n ≥ 3. This special type of Ja...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1999
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-99-02223-0