Displaying similar documents to “The metrical theory of complex continued fractions”

Symmetry and folding of continued fractions

Alfred J. Van der Poorten (2002)

Journal de théorie des nombres de Bordeaux

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Michel Mendès France's “Folding Lemma” for continued fraction expansions provides an unusual explanation for the well known symmetry in the expansion of a quadratic irrational integer.

A note on Howe's oscillator semigroup

Joachim Hilgert (1989)

Annales de l'institut Fourier

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Analytic extensions of the metaplectic representation by integral operators of Gaussian type have been calculated in the L 2 ( n ) and the Bargmann-Fock realisations by Howe [How2] and Brunet-Kramer [Brunet-Kramer, Reports on Math. Phys., 17 (1980), 205-215]], respectively. In this paper we show that the resulting semigroups of operators are isomorphic and calculate the intertwining operator.