Comments on the height reducing property

• Autorzy: Shigeki Akiyama , Toufik Zaimi
• Języki publikacji: EN

Abstrakty

EN

A complex number α is said to satisfy the height reducing property if there is a finite subset, say F, of the ring ℤ of the rational integers such that ℤ[α] = F[α]. This property has been considered by several authors, especially in contexts related to self affine tilings and expansions of real numbers in non-integer bases. We prove that a number satisfying the height reducing property, is an algebraic number whose conjugates, over the field of the rationals, are all of modulus one, or all of modulus greater than one. Expecting the converse of the last statement is true, we show some theoretical and experimental results, which support this conjecture.

Słowa kluczowe

EN

Roots of polynomials; Height of polynomials; Special algebraic numbers; Quantitative Kronecker’s approximation theorem

Kategorie tematyczne

• 11A63: Radix representation; digital problems
• 11R06: PV-numbers and generalizations; other special algebraic numbers; Mahler measure
• 11R04: Algebraic numbers; rings of algebraic integers
• 12D10: Polynomials: location of zeros (algebraic theorems)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 9
• Strony: 1616-1627

Daty

wydano

2013-09-01

online

2013-06-28

Twórcy

autor

Shigeki Akiyama

• University of Tsukuba

autor

Toufik Zaimi

• Larbi Ben M’hidi University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0262-4