| Abstract: |
| In number theory, continued fractions are essential tools because they provide distinct representations of real numbers and provide information about their characteristics. Regular continued fractions have been examined in great detail, but less research has been carried out on their semi-regular continued fractions, which are produced from the sequences of alternating plus and minus ones.
In this talk, attention is paid to the structure and features of semi-regular continued fractions through the lens of dimension theory. A key result is established concerning the Hausdorff dimension of number sets with partial quotients that increase more rapidly than a specified rate. Additionally, numerical analyses are conducted to highlight the distinctions between regular and semi-regular continued fractions, offering insights into potential future directions in this area. |
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