COUVEIGNES, Jean-Marc; EDIXHOVEN, Bas

doi:10.4171/119

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COUVEIGNES, Jean-Marc
Institut de Mathématiques de Bordeaux [IMB]
Laboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA]
Lithe and fast algorithmic number theory [LFANT]
Université de Bordeaux [UB]
Centre National de la Recherche Scientifique [CNRS]
Institut National de Recherche en Informatique et en Automatique [Inria]
Institut Polytechnique de Bordeaux [Bordeaux INP]

EDIXHOVEN, Bas
Mathematical institute

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Geometry and Arithmetic, Geometry and Arithmetic. 2012p. 91-112

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This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations with modular curves and their Jacobians. These approximations are done in polynomial time in the dimension and the required number of significant digits. We explain the main ideas of how the approximations are done, illustrating them with examples, and we sketch some applications in number theory.< Leer menos

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Approximate computations with modular curves

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