Computing the effectively computable bound in Baker's inequality for linear forms in logarithms

A. J. Van Der Poorten, J. H. Loxton

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

For certain number theoretical applications, it is useful to actually compute the effectively computable constant which appears in Baker's inequality for linear forms in logarithms. In this note, we carry out such a detailed computation, obtaining bounds which are the best known and, in some respects, the best possible. We show inter alia that if the algebraic numbers α1, …, αn all lie in an algebraic number field of degree D and satisfy a certain independence condition, then for some n0(D) which is explicitly computed, the inequalities (in the standard notation) [formula omitted] have no solution in rational integers b1, …, bn (bn ≠ 0) of absolute value at most B, whenever n ≥ n0(D). The very favourable dependence on n is particularly useful.

Original languageEnglish
Pages (from-to)33-57
Number of pages25
JournalBulletin of the Australian Mathematical Society
Volume15
Issue number1
DOIs
Publication statusPublished - 1976
Externally publishedYes

Bibliographical note

Corrigenda and addenda can be found in Bulletin of the Australian Mathematical Society, 17(1), pp. 151-155, 1977.
https://doi.org/10.1017/S0004972700025600

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