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Generalizations of the Markoff–Hurwitz equations over finite fields

✍ Scribed by Ioulia Baoulina

Book ID
104024642
Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
180 KB
Volume
118
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

✦ Synopsis

Let N q be the number of solutions of the equation

over the finite field F q = F p s . L. Carlitz found formulas for N q for n = 3 and for n = 4 and q ≡ 3 (mod 4). He also expressed N q for n = 4 and q ≡ 1 (mod 4) in terms of Jacobsthal sums. In an earlier paper, we found formulas for N q when d = gcd(n -2, (q -1)/2) = 1 or 2. In this paper, we find formulas for N q when d = 4 and p ≡ 7 (mod 8); and when there exists an l such that p l ≡ -1 (mod 2d).

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