Displaying similar documents to “Computing special values of motivic L -functions.”

An objective and practical method for describing and understanding ratios

D. H. Fowler (1993)

Mathématiques et Sciences Humaines

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This article explores the use of the euclidian algorithm as a most useful way of handling ratios, especially when good rational approximations are required. Illustrations are taken from a discussion of the analysis of greek architecture by J.J Coulton. Although this is intended as a practical account, some discussions of theoretical aspects are included, and also of the relationship of this procedure to a new interpretation of early greek mathematics.

A two-dimensional continued fraction algorithm with Lagrange and Dirichlet properties

Christian Drouin (2014)

Journal de Théorie des Nombres de Bordeaux

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A Lagrange Theorem in dimension 2 is proved in this paper, for a particular two dimensional continued fraction algorithm, with a very natural geometrical definition. Dirichlet type properties for the convergence of this algorithm are also proved. These properties proceed from a geometrical quality of the algorithm. The links between all these properties are studied. In relation with this algorithm, some references are given to the works of various authors, in the domain of multidimensional...