We study quadratic approximations for two families of hyperquadratic continued fractions in the field of Laurent series over a finite field. As the first application, we give the answer to a question of the second author concerning Diophantine …
As an analogue of Mahler’s classification for real numbers, Bundschuh introduced a classification for Laurent series over a finite field, divided into $A,S,T,U$-numbers. It is known that each of the sets of $A,S,U$-numbers is nonempty. On the other …
In this paper, we study the properties of Diophantine exponents $w_n$ and $w_n^{∗}$ for Laurent series over a finite field. We prove that for an integer $n \geq 1$ and a rational number $w2n-1$, there exist a strictly increasing sequence of positive …
In this paper, we study Diophantine exponents $w_n$ and $w_n^{∗}$ for Laurent series over a finite field. Especially, we deal with the case $n = 2$, that is, quadratic approximation. We first show that the range of the function $w_2 − w_2^{*}$ is …
We establish a new transcendence criterion of $p$-adic continued fractions which are called Ruban continued fractions. By this result, we give explicit transcendental Ruban continued fractions with bounded $p$-adic absolute value of partial …
In this paper, we study a relation between digits of $p$-adic numbers and Mahler's classification. We show that an irrational $p$-adic number whose digits are automatic, primitive morphic, or Sturmian is an $S$-, $T$-, or $U_1$-number in the sense …