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A transcendence measure for E-functions

Published online by Cambridge University Press:  26 February 2010

Serge Lang
Serge Lang
Affiliation:
Columbia University, New York, U.S.A.
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Extract

Siegel defined an E-function to be a function which admits a power series expansion

with complex coefficients βn, belonging to some algebraic number field K (of finite degree over the rationals Q), satisfying the following conditions:

(i) Given ε > 0, the maximum of the absolute values of the conjugates of βn, satisfies

Type
Research Article
Information
Mathematika , Volume 9 , Issue 2 , December 1962 , pp. 157 - 161
Copyright
Copyright © University College London 1962

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References

1. Mahler, K., On a theorem of Shidlovsky, Mimeographed notes (Amsterdam, 1959).Google Scholar
2. Shidlovsky, A. V., “On a criterion of algebraic independence …” (in Russian), Izvestia Akademia Nauk USSR, 23 (1959), 35–66.Google Scholar
3. Siegel, C. L., “Über einige anwendungen diophantischer approximationen”, Abhandlungen der Preussischen Akademie der Wissenschaften (1929), 1–41.Google Scholar
4. Siegel, C. L., “Transcendental numbers”, Annals of Mathematics Studies No. 16 (Princeton, 1949).Google Scholar