Displaying similar documents to “Dirichlet and Neumann problems for string equation, Poncelet problem and Pell-Abel equation.”

Computing fundamental domains for Fuchsian groups

John Voight (2009)

Journal de Théorie des Nombres de Bordeaux

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We exhibit an algorithm to compute a Dirichlet domain for a Fuchsian group Γ with cofinite area. As a consequence, we compute the invariants of Γ , including an explicit finite presentation for Γ .

On the discrete logarithm problem for plane curves

Claus Diem (2012)

Journal de Théorie des Nombres de Bordeaux

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In this article the discrete logarithm problem in degree 0 class groups of curves over finite fields given by plane models is studied. It is proven that the discrete logarithm problem for non-hyperelliptic curves of genus 3 (given by plane models of degree 4) can be solved in an expected time of O ˜ ( q ) , where q is the cardinality of the ground field. Moreover, it is proven that for every fixed natural number d 4 the following holds: We consider the discrete logarithm problem for curves given...