논문KCI 등재
DISCRETE MEASURES WITH DENSE JUMPS INDUCED BY STURMIAN DIRICHLET SERIES
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초록
Let (sα(n))n≥1 be the lexicographically greatest Sturmian word of slope α > 0. For a fixed σ > 1, we consider Dirichlet series of the form νσ(α) := ∑∞ n=1 sα(n)n−σ. This paper studies the singular properties of the real function νσ, and the Lebesgue-Stieltjes measure whose distribution is given by νσ.
Abstract
Let (sα(n))n≥1 be the lexicographically greatest Sturmian word of slope α > 0. For a fixed σ > 1, we consider Dirichlet series of the form νσ(α) := ∑∞ n=1 sα(n)n−σ. This paper studies the singular properties of the real function νσ, and the Lebesgue-Stieltjes measure whose distribution is given by νσ.
참고문헌 (5)
- T. M. Apostol, "Introduction to Analytic Number Theory" (1976), Springer-Verlag
- D. Y. Kwon, "Moments of discrete measures with dense jumps induced by β-expansions", J. Math. Anal. Appl, 399(1), pp.1~11 (2013)
- D. Y. Kwon, "A one-parameter family of Dirichlet series whose coefficients are Sturmian words", J. Number Theory, 147, pp.824~835 (2015)
- M. Lothaire, "Algebraic Combinatorics on Words" (2002), Cambridge University Press
- M. Morse, "Symbolic dynamics II. Sturmian trajectories", Amer. J. Math, 62, pp.1~42 (1940)
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