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BIRS Workshop Lecture Videos

The Fricke-Macbeath curve Top, Jaap

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(Joint with Carlo Verschoor.) The curve in question was introduced as a Riemann surface by R. Fricke in 1899 and as an algebraic curve by A.M. Macbeath in 1965. It is an example of a Shimura curve; moreover, it is the unique Hurwitz curve of genus 7. Only quite recently models of it over the rational numbers were found. We describe how to compute the number of rational points on reductions mod p of these models.

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