The distribution of reduced numbers in an ideal of a real cubic number field |
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Authors: | J Wolfskill |
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Institution: | Department of Mathematics, Michigan State University, East Lansing, Michigan 48824 USA |
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Abstract: | Let K be a real but not totally real field of degree three over Q, and let A be an ideal in K. It is proved that the reduced numbers in A (i.e., numbers α with α > 1 and ?1 < Re α(j) < 0 for all conjugates α(j) ≠ α) are dense in a set of intervals of constant length, and no reduced numbers in A occur in the gaps between these intervals. In fact, the intervals are determined explicitly, and criteria are given for when the reduced numbers in A actually are dense in the whole of 1, ∞). |
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