A one-parameter family of Dirichlet series whose coefficients are Sturmian words

TextGiven α>0α>0, let (sα(n))n≥1(sα(n))n≥1 be the lexicographically greatest Sturmian word of slope α  . We study Dirichlet series with sα(n)sα(n) coefficients. Its continuity and differentiability in α are investigated. As a consequence, we obtain another kind of singular function whose differentiability rests upon Diophantine approximation.VideoFor a video summary of this paper, please visit http://youtu.be/V9o-2wIJWVQ.