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Canonical bases for cyclotomic fields

✍ Scribed by Wieb Bosma

Publisher
Springer
Year
1990
Tongue
English
Weight
573 KB
Volume
1
Category
Article
ISSN
0938-1279

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Let `be a primitive 2 m th root of unity. We prove that Z[:]=Z [`] if and only if :=n\`i for some n, i # Z, i odd. This is the first example of number fields of arbitrarily large degree for which all power bases for the ring of integers are known. 2001 Academic Press ## 1. Introduction A number f

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Let p be an odd prime and q = p m , where m is a positive integer. Let ΞΆ be a primitive qth root of unity, and O q be the ring of integers in the cyclotomic field Q(ΞΆ ). We prove that if O q = Z[Ξ±] and gcd(h + q , p(p -1)/2) = 1, where h + q is the class number of Q(ΞΆ + ΞΆ -1 ), then an integer trans

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Let p be an odd prime and O p be the ring of integers in the cyclotomic field Q(`), where `is a primitive p th root of unity. Then O p =Z[:] if :=`, 1Γ‚(1+`), or one of the conjugates of these two elements. In 1988, Bremner [3] conjectured that up to integer translation there are no further generator