Cyclotomic units over finite fields |
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Authors: | Klaus Hoechsmann |
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Institution: | 1. Department of Mathematics, University of British Columbia, V6T 1 Y4, Vancouver, Canada
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Abstract: | Let ζ be a primitivesp-th root of unity for a primep>2, and consider the group Ω(ζ) of cyclotomic units in the ringR(ζ)=ℒζ+ζ-1]. This paper deals with the image of Ω(ζ) in the unit group ofR(ζ)/qR(ζ), whereq is a prime ≠p. In particular, it obtains criteria for this image to be essentially everything, and a lower bound on the density of primesp (withq fixed) for which it cannot be. These results have a direct bearing on previous work about units in integral group rings for
cyclic groups of orderpq.
Work supported in part by an operating grant from NSERC (Canada). |
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Keywords: | AMS Subject Classifications" target="_blank">AMS Subject Classifications 11T22 20C05 |
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