| Popis: |
A formula giving the exact error term for convergents of quadratic numbers is given. This formula is applied to Markoff forms and Markoff irrationalities: characterization of the smallest values of the form (the minimum being the corresponding Markoff number), mapped bijectively to the conjugates of the corresponding Christoffel word; a new proof of the result giving the ranks of the good convergents of the Markoff irrationalities; a refinement of Markoff's classification of the latter numbers. Other applications appear in the article. |
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