Representing algebraic integers as linear combinations of units |
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Authors: | D. Dombek L. Hajdu A. Pethő |
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Affiliation: | 1. Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120?00?, Prague 2, Czech Republic 2. Institute of Mathematics, University of Debrecen, P.O. Box 12, Debrecen, 4010, Hungary 3. Department of Computer Science, University of Debrecen, P.O. Box 12, Debrecen, 4010, Hungary
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Abstract: | In this paper we consider representations of algebraic integers of a number field as linear combinations of units with coefficients coming from a fixed small set, and as sums of elements having small norms in absolute value. These theorems can be viewed as results concerning a generalization of the so-called unit sum number problem, as well. Beside these, extending previous related results we give an upper bound for the length of arithmetic progressions of (t) -term sums of algebraic integers having small norms in absolute value. |
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