# Comments on the height reducing property

Open Mathematics (2013)

- Volume: 11, Issue: 9, page 1616-1627
- ISSN: 2391-5455

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topShigeki Akiyama, and Toufik Zaimi. "Comments on the height reducing property." Open Mathematics 11.9 (2013): 1616-1627. <http://eudml.org/doc/269056>.

@article{ShigekiAkiyama2013,

abstract = {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.},

author = {Shigeki Akiyama, Toufik Zaimi},

journal = {Open Mathematics},

keywords = {Roots of polynomials; Height of polynomials; Special algebraic numbers; Quantitative Kronecker’s approximation theorem; roots of polynomials; height of polynomials; special algebraic numbers; quantitative Kronecker's approximation theorem},

language = {eng},

number = {9},

pages = {1616-1627},

title = {Comments on the height reducing property},

url = {http://eudml.org/doc/269056},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Shigeki Akiyama

AU - Toufik Zaimi

TI - Comments on the height reducing property

JO - Open Mathematics

PY - 2013

VL - 11

IS - 9

SP - 1616

EP - 1627

AB - 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.

LA - eng

KW - Roots of polynomials; Height of polynomials; Special algebraic numbers; Quantitative Kronecker’s approximation theorem; roots of polynomials; height of polynomials; special algebraic numbers; quantitative Kronecker's approximation theorem

UR - http://eudml.org/doc/269056

ER -

## References

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