On the Number of Points on a Plane Algebraic Curve over $GF(q)[t]/t^n$

Abstract

A general formula is obtained for the number of points lying on a plane algebraic curve over the finite local ring $\mathrm{G}\mathrm{F}(q)[t]/(t^n)$ ($n>1$) whose equation has coefficients in $\mathrm{G}\mathrm{F}(q)$ and under the restriction that it has only simple and ordinary singular points.