有限域上广义Markoff-Hurwitz-type方程的有理点个数(The number of solutions of generalized Markoff-Hurwitz-type equations over finite fields)

Abstract

Let Nq denote the number of solutions of the generalized Markoff-Hurwitz-type equations over the finite field , where n≥2, mi, k, kj and t≥n are positive integers, ai, , for 1≤i≤n and 1≤j≤t. Recently, some researches considered the above equation with k = k1 = … = kt = 1 and obtained some generalizations of Carlitz's results. In this paper, we determine Nq explicitly in some other cases. This extends the previous conclusions.

Keywords

• finite field
• rational point
• markoff-hurwitz-type equations