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<p>We study some arithmetic properties on the set of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-polynomials. Firstly, we give a sufficient condition for the finiteness of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(L_{\odot }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mo>⊙</mo> </msub> </math></EquationSource> </InlineEquation> which represent the maximal finite shift after the comma for the product of two beta-polynomials. Secondly, we give explicit values of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(L_{\odot }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mo>⊙</mo> </msub> </math></EquationSource> </InlineEquation> for families of Pisot basis.</p>

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Computation of \(L_{\odot }\) for algebraic series over \({\mathbb {F}}_q((X^{-1}))\)

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • R. Ghorbel,
  • S. Zouari

摘要

We study some arithmetic properties on the set of \(\beta \) β -polynomials. Firstly, we give a sufficient condition for the finiteness of \(L_{\odot }\) L ⊙ which represent the maximal finite shift after the comma for the product of two beta-polynomials. Secondly, we give explicit values of \(L_{\odot }\) L ⊙ for families of Pisot basis.