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Further results on rational points of the curve y(qn) - y = gamma xqh+1 - alpha over F-qm

2016-06-01
Cosgun, Ayhan
Özbudak, Ferruh
SAYGI, ZÜLFÜKAR
Let q be a positive power of a prime number. For arbitrary positive integers h, n, m with n dividing m and arbitrary gamma, alpha is an element of F-qm with gamma not equal 0 the number of F-qm - rational points of the curve y(qn) - y = gamma x(qh+1) - alpha is determined in many cases (Ozbudak and Saygi, in: Larcher et al. (eds.) Applied algebra and number theory, 2014) with odd q. In this paper we complete some of the remaining cases for odd q and we also present analogous results for even q.