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Journal of the Ramanujan Mathematical Society

Volume 34, Issue 1, March 2019  pp. 143–150.

Distribution of prime ideals across ideal classes in the class groups

Authors:  Prem Prakash Pandey
Author institution:Department of Mathematics, IISER Berhampur, Engineering School Road, Khodasingi, Brahmapur 760 010, India

Summary:  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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