On the representation of integers as linear combinations of consecutive values of a polynomial |
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Authors: | Jacques Boulanger Jean-Luc Chabert |
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Affiliation: | Department of Mathematics, Université de Picardie, 80039 Amiens, France, LAMFA CNRS-UMR 6140, France ; Department of Mathematics, Université de Picardie, 80039 Amiens, France, LAMFA CNRS-UMR 6140, France |
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Abstract: | Let be a cyclotomic field with ring of integers and let be a polynomial whose values on belong to . If the ideal of generated by the values of on is itself, then every algebraic integer of may be written in the following form: for some integer , where the 's are roots of unity of . Moreover, there are two effective constants and such that the least integer (for a fixed ) is less than , where |
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Keywords: | |
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