Affiliation:
1. The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
Abstract
Let Nq be the number of solutions to the equation [Formula: see text] over the finite field 𝔽q = 𝔽ps. Carlitz found formulas for Nq when m1 = ⋯ = mn = 1, k = 2, n = 3 or 4, p > 2; and when m1 = ⋯ = mn = 2, k = 1, n = 3 or 4, p > 2. In earlier papers, we obtained some generalizations of Carlitz's results. In this paper, we find formulas for Nq when -1 is a power of p modulo dD, where D = lcm [d1,…,dn], [Formula: see text], M = lcm [m1,…,mn], dj = gcd (mj,q - 1), 1 ≤ j ≤ n.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
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