On Simultaneous Approximation of Algebraic Power Series over a Finite Field
Khalil Ayadi, Chiheb Ben Bechir, Samir Elkadri · P-Adic Numbers Ultrametric Analysis and Applications · 2024
In 1970, W. M. Schmidt [6] generalized Roth’s well-known theorem on rational approximation to a single algebraic irrational, to include simultaneous rational approximation for a given $$n$$ algebraic irrationals. As no analogue of Roth’s theorem for algebraic irrational power series over a finite field exists, we will show that there is no analogue of Schmidt’s theorem for such $$n$$ elements.