On Sums of Powers of Inverse Complete Quotients
نویسندگان
چکیده
For an irrational number x, let xn denote its n-th continued fraction inverse complete quotient, obtained by deleting the first n partial quotients. For any positive real number r, we establish the optimal linear bound on the sum of the r-th powers of the first n complete quotients. That is, we find the smallest constants α(r),β(r) such that x1 + . . . + x r n < α(r)n + β(r) for all n ≥ 1 and all irrationals x.
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