Gauss Sums of Cubic Characters over Fpr, p Odd
نویسندگان
چکیده
منابع مشابه
Kummer’s Conjecture for Cubic Gauss Sums
for primes p ≡ 1 (mod 3) up to 500, and found that Sp/(2√p) lay in the intervals [−1,− 12 ], (− 12 , 12 ), [ 1 2 , 1] with frequencies approximately in the ratio 1 : 2 : 3. He conjectured, somewhat hesitantly, that this might be true asymptotically. Kummer’s conjecture was disproved by Heath-Brown and Patterson [4]. In order to state their result we must introduce a little notation. Let ω = exp...
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متن کاملEXPLICIT EVALUATION OF CERTAIN EXPONENTIAL SUMS OF QUADRATIC FUNCTIONS OVER Fpn, p ODD
x∈Fpn en(f(x)), where en(y) = e2πiTrn(y)/p, y ∈ Fpn , Trn = TrFpn/Fp . There is an effective way to compute the nullity of the quadratic form Trmn(f(x)) for all integer m > 0. Assuming that all such nullities are known, we find relative formulas for S(f,mn) in terms of S(f, n) when νp(m) ≤ min{νp(αi) : 1 ≤ i ≤ k}, where νp is the p-adic order. We also find an explicit formula for S(f, n) when ν...
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ژورنال
عنوان ژورنال: Bulletin of the Polish Academy of Sciences Mathematics
سال: 2012
ISSN: 0239-7269,1732-8985
DOI: 10.4064/ba60-1-1