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Distribution of Prime Ideals Across Ideal Classes in the Class Groups
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In this article we investigate the distribution of prime ideals of residue degree bigger than one across the ideal classes in the class group of a number field L. A criterion for the class group of L being generated by the classes of prime ideals of residue degree f > 1 is provided. Further, some consequences of this study on the solvability of norm equations for L/ℚ and on the problem of finding annihilators for relative extensions are discussed.
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