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- Cho, Peter J.
- Lab for L-functions and arithmetic
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EFFECTIVE PRIME IDEAL THEOREM AND EXPONENTS OF IDEAL CLASS GROUPS
- Author(s)
- Cho, Peter J., Kim, Henry H.
- Issued Date
- 2014-12
- Citation
- QUARTERLY JOURNAL OF MATHEMATICS, v.65, no.4, pp.1179 - 1193
- Abstract
- For a family of G-fields K, we show an effective prime ideal theorem with probability 1. Namely, outside a density zero set, pi(x, K)=Li(x)+O(x/(log x)(2)) for xa parts per thousand yen(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
- Publisher
- OXFORD UNIV PRESS
- ISSN
- 0033-5606
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