Multiplicative functions and $k$-automatic sequences

Yazdani, Soroosh

doi:10.5802/jtnb.342

Cited by 18 publications

(25 citation statements)

References 5 publications

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“…In light of Christol's theorem, it is natural to ask if one can characterize automatic multiplicative functions. Partial progress has been made by Yazdani [26] and Coons [13]. All examples of automatic multiplicative functions found thus far have the property that they are well behaved on the set of prime powers.…”

Section: Discussionmentioning

confidence: 99%

Transcendence of generating functions whose coefficients are multiplicative

Bell

Bruin

Coons

2012

Trans. Amer. Math. Soc.

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Section: Discussionmentioning

confidence: 99%

Transcendence of generating functions whose coefficients are multiplicative

Bell

Bruin

Coons

2012

Trans. Amer. Math. Soc.

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“…The transcendence of the series ∞ n=1 f (z)z n over Z(z) for f equal to each of the multiplicative functions τ k , σ k , and ϕ was shown by Yazdani [12]; the case f = µ was previously treated by Allouche [1] using a deep result of Cobham [7]. While transcendence results on power series are readily available, there are many open questions concerning their special values.…”

Section: Corollary 2 If µ Is the Möbius Function Then The Seriesmentioning

confidence: 99%

Transcendence of power series for some number theoretic functions

Borwein

Coons

2008

Proc. Amer. Math. Soc.

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Abstract. We give a new proof of Fatou's theorem: if an algebraic function has a power series expansion with bounded integer coefficients, then it must be a rational function. This result is applied to show that for any non-trivial completely multiplicative function from N to {−1, 1}, the series (Fatou, 1906). A power series whose coefficients take only finitely many values is either rational or transcendental.In this paper, we give a new proof of Fatou's theorem and apply it to show that various power series are transcendental; as specific examples we show the transcendence of the series

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“…In particular, the question of classifying automatic multiplicative sequences has been investigated by a number of authors, including [1,2,7,8,12,14]. The interplay between multiplicative and automatic sequences is studied also in [3,5,11,13,15], among others.…”

Section: Introductionmentioning

confidence: 99%