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TITLE The least non-split prime in a number field
KIAS AUTHORS Kim, Henry H.
JOURNAL ARCHIV DER MATHEMATIK, 2021
ARCHIVE  
ABSTRACT Let K be an S-n-field (n <= 5) with discriminant d(K). Let n(K) be the least prime which does not split completely in K. We prove unconditionally that n(K) = O(log vertical bar d(K)vertical bar), except for O(Xexp(- clogX/log logX)) fields for some constant c > 0. We also prove that the exceptional set is optimal, and that for any eta > 0, the S-n-fields such that n(K) >> (log vertical bar d(K)vertical bar)(1+eta) are very rare.
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