Publication Date:
2014-11-20
Description:
For a family of G -fields K , we show an effective prime ideal theorem with probability 1. Namely, outside a density zero set, ( x , K )=Li( x )+ O ( x /(log x ) 2 ) for x ≥(log d K ) c for some c depending on G . Using the effective prime ideal theorem, we show that the exponents e K of the ideal class groups of a family of G -fields increase along with d K with probability 1.
Print ISSN:
0033-5606
Electronic ISSN:
1464-3847
Topics:
Mathematics
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