Article contents
Analytic continuation of power series whose coefficients belong to an algebraic number field
Published online by Cambridge University Press: 26 February 2010
Extract
An old theorem of Pólya and Carlson [2] states that, if the power series has rational integer coefficients, positive radius of convergence, and can be continued analytically to a region that contains points outside the closed unit disc, then the function that the power series represents is rational. This result has been extended in a number of ways (cf. e.g. Petersson [4]). The present note gives a new extension based on a recent theorem of Güting [3]. My thanks to Professors Henry Helson and Raphael Robinson for introducing me to this subject.
- Type
- Research Article
- Information
- Copyright
- Copyright © University College London 1969
References
- 1
- Cited by