We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
$U$-NUMBERS IN FIELDS OF FORMAL POWER SERIES OVER FINITE FIELDS
In the field 
$\mathbb{K}$ of formal power series over a finite field 
$K$, we consider some lacunary power series with algebraic coefficients in a finite extension of 
$K(x)$. We show that the values of these series at nonzero algebraic arguments in 
$\mathbb{K}$ are 
$U$-numbers.
In this note, we prove that for any 
${\it\nu}>0$, there is no lacunary entire function 
$f(z)\in \mathbb{Q}[[z]]$ such that 
$f(\mathbb{Q})\subseteq \mathbb{Q}$ and 
$\text{den}f(p/q)\ll q^{{\it\nu}}$, for all sufficiently large 
$q$.
