Complex Numbers with Bounded Partial Quotients
نویسندگان
چکیده
Conjecturally, the only real algebraic numbers with bounded partial quotients in their regular continued fraction expansion are rationals and quadratic irrationals. We show that the corresponding statement is not true for complex algebraic numbers in a very strong sense, by constructing for every even degree d algebraic numbers of degree d that have bounded complex partial quotients in their Hurwitz continued fraction expansion. The Hurwitz expansion is the generalization of the nearest integer continued fraction for complex numbers. In the case of real numbers the boundedness of regular and nearest integer partial quotients is equivalent.
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