| 1. |
- Klurman, Oleksiy, et al.
(author)
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A note on multiplicative automatic sequences
- 2019
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In: Comptes rendus. Mathematique. - : ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER. - 1631-073X .- 1778-3569. ; 357:10, s. 752-755
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Journal article (peer-reviewed)abstract
- We prove that any q-automatic completely multiplicative function f: N -> C essentially coincides with a Dirichlet character. This answers a question of J.-P. Allouche and L. Gold-makher and confirms a conjecture of J. Bell, N. Bruin and M. Coons for completely multiplicative functions. Further, assuming GRH, the methods allow us to replace completely multiplicative functions with multiplicative functions.
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| 2. |
- Klurman, Oleksiy, et al.
(author)
-
V. Markov's problem for k-absolutely monotone polynomials and applications
- 2019
-
In: Jaen Journal on Approximation. - : Universidad de Jaen. - 1889-3066 .- 1989-7251. ; 11:1-2, s. 139-149
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Journal article (peer-reviewed)abstract
- We consider the classical problem of maximizing the value of the derivative of a polynomial at a given point x0 j [-1,1]. The corresponding extremal problem for general polynomials in the uniform norm was solved by V. Markov. In this paper, we consider the analog of this problem for k-bsolutely monotone polynomials. As a consequence, we solve the analog of V. Markov' problem, find the exact constant in Bernstein' inequality and give a new proof of A. Markov' inequality for monotone polynomials.
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