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RADIAL ASYMPTOTICS OF GENERATING FUNCTIONS OF k-REGULAR SEQUENCES

Part of: Series expansions

Published online by Cambridge University Press:  13 September 2024

MICHAEL COONS  and
JOHN LIND
MICHAEL COONS*
Affiliation:
California State University, 400 West First Street, Chico, California 95929, USA
JOHN LIND
Affiliation:
California State University, 400 West First Street, Chico, California 95929, USA e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

We give a new proof of a theorem of Bell and Coons [‘Transcendence tests for Mahler functions’, Proc. Amer. Math. Soc. 145(3) (2017), 1061–1070] on the leading order radial asymptotics of Mahler functions that are the generating functions of regular sequences. Our method allows us to provide a description of the oscillations whose existence was shown by Bell and Coons. This extends very recent results of Poulet and Rivoal [‘Radial behavior of Mahler functions’, Int. J. Number Theory, to appear].

Keywords

automatic sequencesregular sequencesMahler functionsDirichlet series

MSC classification

Primary: 30B30: Boundary behavior of power series, over-convergence
Secondary: 30B50: Dirichlet series and other series expansions, exponential series 39B32: Equations for complex functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 110 , Issue 3 , December 2024 , pp. 528 - 534
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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