Adamczewski, Boris; Bell, Jason P. A problem about Mahler functions. (English) Zbl 1432.11086 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 17, No. 4, 1301-1355 (2017). Summary: Let \(K\) be a field of characteristic zero and \(k\) and \(l\) be two multiplicatively independent positive integers. We prove the following result that was conjectured by J. H. Loxton and A. J. van der Poorten [J. Reine Angew. Math. 330, 159–172 (1982; Zbl 0468.10019); ibid. 392, 57–69 (1988; Zbl 0656.10033)] during the Eighties: a power series \(F(z)\in K[[z]]\) satisfies both a \(k\)- and a \(l\)-Mahler-type functional equation if and only if it is a rational function. Cited in 2 ReviewsCited in 19 Documents MSC: 11J81 Transcendence (general theory) 11B85 Automata sequences 65Q20 Numerical methods for functional equations Keywords:Mahler functions Citations:Zbl 0468.10019; Zbl 0656.10033 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link