Timeline for Error in an argument using spectral theory

8 events

when toggle format	what		by	license	comment
May 13 at 11:42	history	edited	kaleidoscop	CC BY-SA 4.0	updated in view of the comments
May 13 at 11:38	comment	added	kaleidoscop		Right, probably the fastest way, thanks
May 13 at 11:20	comment	added	Wojowu		An easy way to see this sequence is not periodic is that the density of $k$ for which $\xi(k)=1$ is equal to $1/\sqrt{2}$.
May 13 at 9:42	history	edited	kaleidoscop	CC BY-SA 4.0	missing words
May 13 at 9:41	comment	added	kaleidoscop		Thanks, I expected that. I am not a specialist of spectral theory and I would really need to understand how I use it wrong here.
May 13 at 9:32	comment	added	Carl-Fredrik Nyberg Brodda		No, this is a Sturmian word (in your example, the word is the fixed point of the morphism $0 \mapsto 1$ and $1 \mapsto 110$), and Sturmian words are not periodic, see e.g. Lothaire's book. Note that for $Z = \varphi \mathbb{Z}$, where $\varphi$ is the golden ratio, you get the famous Fibonacci word.
May 13 at 9:20	history	edited	kaleidoscop	CC BY-SA 4.0	clarified what i expect in the answer
May 13 at 8:37	history	asked	kaleidoscop	CC BY-SA 4.0