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We present a new method for computing the zeta function of an algebraic curveover a finite field. The algorithm relies on a trace formula of Harvey to countpoints on a plane model of the curve. The zeta function of the curve is thenobtained by making corrections at singular points. We report on animplementation and provide some examples in MAGMA which demonstrate animprovement over Tuitman's algorithm.

Computing zeta functions of algebraic curves using Harvey's trace formula