Journal of the Ramanujan Mathematical Society

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Distribution of Prime Ideals Across Ideal Classes in the Class Groups


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1 Department of Mathematics, IISER Berhampur, Engineering School Road, Khodasingi, Brahmapur 760 010, India
     

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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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  • Distribution of Prime Ideals Across Ideal Classes in the Class Groups

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Authors

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

Abstract


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.

References