Displaying similar documents to “Sequences of algebraic integers and density modulo  1 ”

Near heaps

Ian Hawthorn, Tim Stokes (2011)

Commentationes Mathematicae Universitatis Carolinae

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On any involuted semigroup ( S , · , ' ) , define the ternary operation [ a b c ] : = a · b ' · c for all a , b , c ∈ S . The resulting ternary algebra ( S , [ ] ) satisfies the para-associativity law [ [ a b c ] d e ] = [ a [ d c b ] e ] = [ a b [ c d e ] ] , which defines the variety of semiheaps. Important subvarieties include generalised heaps, which arise from inverse semigroups, and heaps, which arise from groups. We consider the intermediate variety of near heaps, defined by the additional laws [ a a a ] = a and [ a a b ] = [ b a a ] . Every Clifford semigroup is a near heap when viewed as a semiheap, and we show that the Clifford...

On gaps in Rényi β -expansions of unity for β > 1 an algebraic number

Jean-Louis Verger-Gaugry (2006)

Annales de l’institut Fourier

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Let β > 1 be an algebraic number. We study the strings of zeros (“gaps”) in the Rényi β -expansion   d β ( 1 ) of unity which controls the set ℤ β of β -integers. Using a version of Liouville’s inequality which extends Mahler’s and Güting’s approximation theorems, the strings of zeros in d β ( 1 ) are shown to exhibit a “gappiness” asymptotically bounded above by   log ( M ( β ) ) / log ( β ) , where   M ( β )   is the Mahler measure of   β . The proof of this result provides in a natural way a new classification of algebraic numbers > 1 with classes...

Equidistribution in the dual group of the S -adic integers

Roman Urban (2014)

Czechoslovak Mathematical Journal

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Let X be the quotient group of the S -adele ring of an algebraic number field by the discrete group of S -integers. Given a probability measure μ on X d and an endomorphism T of X d , we consider the relation between uniform distribution of the sequence T n 𝐱 for μ -almost all 𝐱 ∈ X d and the behavior of μ relative to the translations by some rational subgroups of X d . The main result of this note is an extension of the corresponding result for the d -dimensional torus 𝕋 d due to B. Host.

Characterization of E ℱ -subcompactification

Abdolmajid Fattahi, H. R. Ebrahimi Vishki (2006)

Archivum Mathematicum

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For extending the notion of E -algebra, as defined in [2], we present an example of an m-admissible algebra which is not an E - algebra. Then we define E -subcompactification and E ℱ -subcompactification to study the universal E -subcompactification and the universal E ℱ -subcompactification from the function algebras point of view.