## Currently displaying 1 – 5 of 5

Showing per page

Order by Relevance | Title | Year of publication

### Spectral properties of arithmetic functions

Séminaire Delange-Pisot-Poitou. Théorie des nombres

### Infinite Interval Exchange Transformation with Positive Entropy

Publications mathématiques et informatique de Rennes

### Automata, algebraicity and distribution of sequences of powers

Annales de l’institut Fourier

Let $K$ be a finite field of characteristic $p$. Let $K\left(\left(x\right)\right)$ be the field of formal Laurent series $f\left(x\right)$ in $x$ with coefficients in $K$. That is, $f\left(x\right)=\sum _{n={n}_{0}}^{\infty }{f}_{n}{x}^{n}$ with ${n}_{0}\in 𝐙$ and ${f}_{n}\in K\left(n={n}_{0},{n}_{0}+1,\cdots \right)$. We discuss the distribution of ${\left(\left\{{f}^{m}\right\}\right)}_{m=0,1,2,\cdots }$ for $f\in K\left(\left(x\right)\right)$, where $\left\{f\right\}:=\sum _{n=0}^{\infty }{f}_{n}{x}^{n}\in K\left[\left[x\right]\right]$ denotes the nonnegative part of $f\in K\left(\left(x\right)\right)$. This is a little different from the real number case where the fractional part that excludes constant term (digit of order 0) is considered. We give an alternative proof of a result by De Mathan obtaining the generic distribution...

Page 1