ABSTRACT. A p-adic analogue of a recent algebraic independence criterion of Adams is proved. It is then applied to construct Liouville type p-adic continued fractions of the kinds first considered by Ruban, and by Schneider.
Five transcendental elements in function fields of positive characteristic are constructed embracing those previously derived by Wade during 1941-43. The construction results from a careful analysis of the original works of Wade and indicates that this method and its associated technique is still worthy of consideration.
Using simple arguments, we prove algebraic independence of a class of continued fractions extending an earlier result of Bundschuh. We then apply it to give another proof of algebraic independence of numbers whose
g
g
-adic and continued fraction expansions are explicitly known.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.