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A Lower Bound for the Height in Abelian Extensions

✍ Scribed by Francesco Amoroso; Roberto Dvornicich

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 172 KB
Volume: 80
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1999.2451

No coin nor oath required. For personal study only.

✦ Synopsis

We produce an absolute lower bound for the height of the algebraic numbers (different from zero and from the roots of unity) lying in an abelian extension of the rationals. The proof rests on elementary congruences in cyclotomic fields and on Kronecker Weber theorem.

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