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- Cho, Peter J.
- Lab for L-functions and arithmetic
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Probabilistic properties of number fields
- Author(s)
- Cho, Peter J., Kim, Henry H.
- Issued Date
- 2013-12
- Citation
- JOURNAL OF NUMBER THEORY, v.133, no.12, pp.4175 - 4187
- Abstract
- In general a bound on number theoretic invariants under the Generalized Riemann Hypothesis (GRH) for the Dedekind zeta function of a number field K is much stronger than an unconditional one. In this article, we consider three invariants; the residue of zeta(K)(s) at s = 1, the logarithmic derivative of Artin L-function attached to K at s = 1, and the smallest prime which does not split completely in K. We obtain bounds on them just as good as the bounds under GRH except for a density zero set of number fields. (C) 2013 Elsevier Inc. All rights reserved
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- ISSN
- 0022-314X
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