Continued fractions with bounded even-order partial quotients

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00573700" target="_blank" >RIV/61389005:_____/23:00573700 - isvavai.cz</a>
Alternative codes found
RIV/61988987:17310/23:A2402KRM
Result on the web
<a href="https://doi.org/10.1007/s11139-023-00741-1" target="_blank" >https://doi.org/10.1007/s11139-023-00741-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11139-023-00741-1" target="_blank" >10.1007/s11139-023-00741-1</a>

Result language
angličtina
Original language name
Continued fractions with bounded even-order partial quotients
Original language description
The paper is concerned with continued fractions having bounded even-order partial quotients. We demonstrate that every real number can be written as a sum of two continued fractions whose even-order partial quotients are equal to 1, and every positive number can be written as a product of two such continued fractions. Then we study the Hausdorff dimension of the set of continued fractions whose even-order partial quotients are all equal to a given positive integer c. Taking in particular c=1, we show that the set of continued fractions with even-order partial quotients equal to 1 has the Hausdorff dimension between 0.732 and 0.819.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA21-07129S" target="_blank" >GA21-07129S: New Effects from Time-Reversal Non-Invariance</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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