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Algebraic independence of the values at algebraic points of a class of functions considered by Mahler

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Wass N. C.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Acknowledgements...................................................................4 I. Introduction § 1.1. Algebraic independence.................................................5 § 1.2. Notation and some estimates..........................................9 II. Formal series § 2.1. A class to which the solution belong..............................11 III. Zero estimates. § 3.1. The general case ........................................................15 § 3.2. Resultants.....................................................................23 § 3.3. The upper triangular case ...........................................26 IV. Preliminaries § 4.1. Ideals............................................................................30 § 4.2. Some lemmas ..............................................................34 V. The main results § 5.1. Hypothesis Hyp(f,α)......................................................41 § 5.2. Conclusions .................................................................45 Appendix.................................................................................53 References.............................................................................60

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1 Wass N. C.

1 1990

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Algebraic independence of the values at algebraic points of a class of functions considered by Mahler