— Let K be a field of characteristic p > 0 and let f(t1, . . . , td) be a power series in d variables with coefficients in K that is algebraic over the field of multivariate rational functions K(t1, . . . , td). We prove a generalization of both Derksen’s recent analogue of the Skolem–Mahler–Lech theorem in positive characteristic and a classical theorem of Christol, by showing that the set of ...

This paper concerns power series of an arithmetic nature that arise in the analysis of divide-and-conquer algorithms. Two key notions are studied: that of B-regular sequence and that of Mahlerian sequence with their associated power series. Firstly we emphasize the link between rational series over the alphabet fx0;x1;:::;xB?1g and B-regular series. Secondly we extend the theorem of Christol, K...

A famous result of Christol gives that a power series $$F(t)=\sum _{n\ge 0} f(n)t^n$$ with coefficients in finite field $$\mathbb {F}_q$$ characteristic p is algebraic over the rational functions t if and only there finite-state automaton accepting base-p digits n as input giving f(n) output for every $$n\ge 0$$ . An extension Christol’s theorem, complete description closure {F}_q(t)$$ , was la...

Abstract Linked Article: Liu et al. Br J Dermatol 2022; 187:948–961.

ABNORMAL bleeding has been recognized as a presenting symptom in multiple myeloma (Wintrobe, 1961) though less frequently encountered than pain, tumours, deformity, pathological fractures and neuralgic or neurological symptoms. Bernard, Inceman, Zara and Christol (1952) comment that haemorrhage is found more frequently as a secondary or terminal feature than as a presenting symptom, but concede...

The paper presents new properties for some functions constructed similarly to the functiol} ry :" N* -N* , the Smarandache function, defined by "In E N*, ry(n) = min{kJk! is divisible by n} "Smarandache's type function" " The Smarandache "I function and its principal properties are already known in the literature of speciality. Other functions were built analogously, among which the following o...