Simultaneous approximation of a real number by all conjugates of an algebraic number
Guillaume Alain (2007)
Acta Arithmetica
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Displaying similar documents to “Effective results for linear equations in two unknowns from a multiplicative division group”
Simultaneous approximation of a real number by all conjugates of an algebraic number
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Gennady Bachman (2003)
Acta Arithmetica
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Acta Arithmetica
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Damien Roy (2008)
Acta Arithmetica
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W. Żelazko (1973)
Colloquium Mathematicae
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Kronecker and his Arithmetical Theory of The Algebraic Equation.
Henry B. Fine (1891/92)
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A. V. Efimov (1989)
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I. A. Shevchuk (1989)
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Electronic Research Announcements of the American Mathematical Society [electronic only]
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Haukkanen, Pentti (1996)
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Haukkanen, Pentti (2003)
International Journal of Mathematics and Mathematical Sciences
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Alex Bijlsma (1983)
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Multiplicative dependence of shifted algebraic numbers
Paulius Drungilas, Artūras Dubickas (2003)
Colloquium Mathematicae
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We show that the set obtained by adding all sufficiently large integers to a fixed quadratic algebraic number is multiplicatively dependent. So also is the set obtained by adding rational numbers to a fixed cubic algebraic number. Similar questions for algebraic numbers of higher degrees are also raised. These are related to the Prouhet-Tarry-Escott type problems and can be applied to the zero-distribution and universality of some zeta-functions.