✦ LIBER ✦

An Effective Version of Belyi's Theorem

✍ Scribed by Lily S. Khadjavi

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 216 KB
Volume: 96
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2001.2748

No coin nor oath required. For personal study only.

✦ Synopsis

We compute bounds on covering maps that arise in Belyi's Theorem. In particular, we construct a library of height properties and then apply it to algorithms that produce Belyi maps. Such maps are used to give coverings from algebraic curves to the projective line ramified over at most three points. The computations here give upper bounds on the degree and coefficients of polynomials and rational functions over the rationals that send a given set of algebraic numbers to the set f0; 1; 1g with the additional property that the only critical values are also contained in f0; 1; 1g.

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