Multiplicative relations in number fields
- 1 February 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 16 (1) , 83-98
- https://doi.org/10.1017/s0004972700023042
Abstract
In this paper, we obtain an explicit form of the currently best known inequality for linear forms in the logarithms of algebraic numbers. The results complete our previous investigations (Bull. Austral. Math. Soc. 15 (1976), 33–57) which were conditional on a certain independence condition on the algebraic numbers. The extra work needed to obtain unconditional results centres on the properties of multiplicative relations in number fields. In particular, we show that a set of multiplicatively dependent algebraic numbers always satisfies a relation with relatively small exponents.Keywords
This publication has 8 references indexed in Scilit:
- Computing the effectively computable bound in Baker's inequality for linear forms in logarithmsBulletin of the Australian Mathematical Society, 1976
- On a Fundamental Inequality in Number TheoryAnnals of Mathematics, 1971
- Algebraic integers near the unit circleActa Arithmetica, 1971
- Linear forms in the logarithms of algebraic numbers (IV)Mathematika, 1968
- A refinement of two theorems of Kronecker.The Michigan Mathematical Journal, 1965
- Approximate formulas for some functions of prime numbersIllinois Journal of Mathematics, 1962
- Sur quelques théorèmes de M. Petrovitch relatifs aux zéros des fonctions analytiquesBulletin de la Société Mathématiques de France, 1905
- Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten.Journal für die reine und angewandte Mathematik (Crelles Journal), 1857