유계인 부분몫을 갖는 대수적 멱급수의 연분수전개

Abstract

It is conjectured that no algebraic real number of degree higher than two has bounded partial quotients in the continued fraction expansion. On the other hand, it is known in many reserches that some algebraic power series of degree higher than two have bounded partial quotients in the continued fraction expansions over finite fields. In this thesis, we choose certain specific equation and calculate explicit continued fraction expansion of its solution so that we find all partial quotients. Moreover, for another specific equation, we show that its solution has partial quotients of unbounded degrees. For these results, we summarize the basics about the formal power series over finite fields and their continued fraction expansions