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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.
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참고문헌 신청
D. Y. Kwon / 2013 / Moments of discrete measures with dense jumps induced by β-expansions / J. Math. Anal. Appl 399 (1) : 1 ~ 11
D. Y. Kwon / 2015 / A one-parameter family of Dirichlet series whose coefficients are Sturmian words / J. Number Theory 147 : 824 ~ 835
M. Lothaire / 2002 / Algebraic Combinatorics on Words / Cambridge University Press
M. Morse / 1940 / Symbolic dynamics II. Sturmian trajectories / Amer. J. Math 62 : 1 ~ 42
T. M. Apostol / 1976 / Introduction to Analytic Number Theory / Springer-Verlag
D. Y. Kwon / 2015 / A one-parameter family of Dirichlet series whose coefficients are Sturmian words / J. Number Theory 147 : 824 ~ 835
M. Lothaire / 2002 / Algebraic Combinatorics on Words / Cambridge University Press
M. Morse / 1940 / Symbolic dynamics II. Sturmian trajectories / Amer. J. Math 62 : 1 ~ 42
T. M. Apostol / 1976 / Introduction to Analytic Number Theory / Springer-Verlag
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