On Error Sum Functions Formed by Convergents of Real Numbers
نویسندگان
چکیده
Let pm/qm denote the m-th convergent (m ≥ 0) from the continued fraction expansion of some real number α. We continue our work on error sum functions defined by E(α) := ∑m≥0 |qmα − pm| and E∗(α) := ∑ m≥0(qmα − pm) by proving a new density result for the values of E and E∗. Moreover, we study the function E with respect to continuity and compute the integral ∫ 1 0 E(α) dα. We also consider generalized error sum functions for the approximation with algebraic numbers of bounded degrees in the sense of Mahler.
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تاریخ انتشار 2011