- Title
- Degree-one Mahler functions: asymptotics, applications and speculations
- Creator
- Coons, Michael
- Relation
- Bulletin of the Australian Mathematical Society Vol. 102, Issue 3, p. 399-409
- Publisher Link
- http://dx.doi.org/10.1017/S0004972720000040
- Publisher
- Cambridge University
- Resource Type
- journal article
- Date
- 2020
- Description
- We present a complete characterisation of the radial asymptotics of degree-one Mahler functions as z approaches roots of unity of degree kn, where k is the base of the Mahler function, as well as some applications concerning transcendence and algebraic independence. For example, we show that the generating function of the Thue–Morse sequence and any Mahler function (to the same base) which has a nonzero Mahler eigenvalue are algebraically independent over C(z). Finally, we discuss asymptotic bounds towards generic points on the unit circle.
- Subject
- transcendence; algebraic independence; radial asymptotics; automatic sequences; Mahler functions
- Identifier
- http://hdl.handle.net/1959.13/1432801
- Identifier
- uon:39110
- Identifier
- ISSN:0004-9727
- Language
- eng
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