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Fractions continues—Sommes de dedekind et formes quadratiques

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Résumé

On étudie les propriétés de symétrie du développement en fraction continue des nombres rationnels en utilisant une représentation matricielle (Théorèmes 1, 4, 6, 7, 8). Lethéorème principal généralise un résultat de Perron. Relation avec la théorie des formes quadratiques (Théorème 12). Application aux sommes de Dedekind (Théorème 11).

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Bibliographie

  1. Perron O.,Die Lehre von der Kettenbrüchen, Chelsea, 1929.

  2. Barkan Ph.,Sur les sommes de Dedekind, C. R. Acad. Sci.,284 (1977), 923–926.

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  3. Rademacher H., Grossald E.,Dedekind Sums. Carus Math. Monographs., Am. Math. Soc., (1972).

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Authors and Affiliations

  1. Département Informatique, Institut Univeritaire de Technologie, Bayonne

    P. Barrucand & M. Duboué

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  1. P. Barrucand
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  2. M. Duboué
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Barrucand, P., Duboué, M. Fractions continues—Sommes de dedekind et formes quadratiques. Rend. Circ. Mat. Palermo 33, 62–84 (1984). https://doi.org/10.1007/BF02844412

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  • DOI: https://doi.org/10.1007/BF02844412

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