Displaying similar documents to “Periodic Jacobi-Perron expansions associated with a unit”

Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R

Ben Salem, N., Ould Ahmed Salem, A., Selmi, B. (2006)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63 Using a convolution structure on the real line associated with the Jacobi-Dunkl differential-difference operator Λα,β given by: Λα,βf(x) = f'(x) + ((2α + 1) coth x + (2β + 1) tanh x) { ( f(x) − f(−x) ) / 2 }, α ≥ β ≥ −1/2 , we define mean-periodic functions associated with Λα,β. We characterize these functions as an expansion series intervening appropriate elementary functions expressed in terms of...

A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm

Jun-ichi Tamura (1992)

Acta Arithmetica

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In this paper, we give transcendental numbers φ and ψ such that (i) both φ and ψ have explicit g-adic expansions, and simultaneously, (ii) the vector t ( φ , ψ ) has an explicit expression in the Jacobi-Perron algorithm (cf. Theorem 1). Our results can be regarded as a higher-dimensional version of some of the results in [1]-[5] (see also [6]-[8], [10], [11]). The numbers φ and ψ have some connection with algebraic numbers with minimal polynomials x³ - kx² - lx - 1 satisfying (1.1) k ≥ l ≥0, k...

Small-sum pairs in abelian groups

Reza Akhtar, Paul Larson (2010)

Journal de Théorie des Nombres de Bordeaux

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Let G be an abelian group and A , B two subsets of equal size k such that A + B and A + A both have size 2 k - 1 . Answering a question of Bihani and Jin, we prove that if A + B is aperiodic or if there exist elements a A and b B such that a + b has a unique expression as an element of A + B and a + a has a unique expression as an element of A + A , then A is a translate of B . We also give an explicit description of the various counterexamples which arise when neither condition holds.

Infinite periodic points of endomorphisms over special confluent rewriting systems

Julien Cassaigne, Pedro V. Silva (2009)

Annales de l’institut Fourier

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We consider endomorphisms of a monoid defined by a special confluent rewriting system that admit a continuous extension to the completion given by reduced infinite words, and study from a dynamical viewpoint the nature of their infinite periodic points. For prefix-convergent endomorphisms and expanding endomorphisms, we determine the structure of the set of all infinite periodic points in terms of adherence values, bound the periods and show that all regular periodic points are attractors. ...