**abstract:**
We consider inhomogeneous Diophantine approximations on the field of formal Laurent series \( \mathbb{F}_q (X^{-1}) \) are studied.

For an fixed \( f \in \mathbb{F}_q((X^{-1})) \setminus \mathbb{F}_q (X) \), we investigate how evenly ${Q f}_{Q in mathbb F_q X}$ modulo $mathbb F_q X$ distributes on the set of the formal Laurent series.
For any $f in mathbb F_q((X^{-1})) setminus mathbb F_q (X)$, balls of center $Q
f$ modulo $mathbb F_q X$ with radius $q^{-n}$, $n = deg(Q)$ cover the set of the formal Laurent series except measure zero set infinitely many times.
But when the radius is not uniformly decreasing, all sequence of balls of which
summation of measure is infinite, cover almost every point if and only if $f$ is of bounded type.
We also discuss some examples $f$'s of unbounded type under monotonicity
restrictions on the size of balls.

Wed 26 Jan, 11:00 - 12:00, Sala Conferenze Centro De Giorgi

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