Normal binomials over algebraic number fields
نویسندگان
چکیده
منابع مشابه
Normal Algebraic Number Fields.
Introduction. In this paper we present a detailed account of the results recently published in the Proceedings of the National Academy of Sciences [29 Our theory is an attempt to generalize the results of the classical class field theory to arbitrary normal fields. In the last analysis, the theory of cyclic extensions Z of an algebraic number field k can be described in terms of cyclic algebras...
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We prove that if xm + axn permutes the prime field Fp, where m > n > 0 and a ∈ Fp, then gcd(m − n, p − 1) > √ p − 1. Conversely, we prove that if q ≥ 4 and m > n > 0 are fixed and satisfy gcd(m − n, q − 1) > 2q(log log q)/ log q, then there exist permutation binomials over Fq of the form xm + axn if and only if gcd(m,n, q − 1) = 1.
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By an algebraic number field we mean a subfield of the algebraic numbers, or an isomorphic copy of such a field. Here we consider questions related to the complexity of determining isomorphism between algebraic number fields. We characterize the algebraic number fields with computable copies. For computable algebraic number fields, we give the complexity of the index sets. We show that the isom...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1980
ISSN: 0022-314X
DOI: 10.1016/0022-314x(80)90023-2