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Power Bases for Cyclotomic Integer Rings

✍ Scribed by Leanne Robertson

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 455 KB
Volume: 69
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1997.2214

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✦ Synopsis

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 :=, 1Â(1+), or one of the conjugates of these two elements. In 1988, Bremner [3] conjectured that up to integer translation there are no further generators for O p and proved that this is indeed the case when p=7. We establish a criterion for verifying Bremner's conjecture for a given regular prime p and use it to prove the conjecture for p 23, p{17. A key step in the proof of the criterion is a determinant formula for the relative class number h & of Q(`).

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