On density modulo 1 of some expressions containing algebraic integers
Roman Urban (2007)
Acta Arithmetica
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Roman Urban (2007)
Acta Arithmetica
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Hajime Kaneko (2012)
Acta Arithmetica
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J. Wójcik (1975)
Acta Arithmetica
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Józef Tabor (1973)
Annales Polonici Mathematici
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R. Stora (1986)
Recherche Coopérative sur Programme n°25
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J. C. Varlet (1975)
Colloquium Mathematicae
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J. Garza, M. I. M. Ishak, C. Pinner (2010)
Acta Arithmetica
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K. Orlov, B. Savić (1983)
Matematički Vesnik
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J. Schmidt (1964)
Colloquium Mathematicae
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Thomas Jarrett
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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.
Robert M. Fossum (1980)
Publications mathématiques et informatique de Rennes
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Charles James Hargreave
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Smirnov, A.L. (2004)
Zapiski Nauchnykh Seminarov POMI
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Stéphane Fischler (2001)
Acta Arithmetica
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G. Lettl (1987)
Colloquium Mathematicae
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Ivan Chajda (2005)
Discussiones Mathematicae - General Algebra and Applications
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We get an interrelation between an algebraic closure system and its conjugated interior system. We introduce the concept of algebraic interior system and we get its representation.