It is shown that there is a constant A and a density one subset S of the positive integers such that, for each , there is some , , so that has all its partial quotients bounded by A.
On montre quʼil existe une constante A et un sous-ensemble S des entiers positifs de densité un, tel que pour tout il y a un entier pour lequel les quotients partiels de sont bornés par A.
Accepted:
Published online:
Jean Bourgain 1; Alex Kontorovich 2
@article{CRMATH_2011__349_9-10_493_0, author = {Jean Bourgain and Alex Kontorovich}, title = {On {Zaremba's} conjecture}, journal = {Comptes Rendus. Math\'ematique}, pages = {493--495}, publisher = {Elsevier}, volume = {349}, number = {9-10}, year = {2011}, doi = {10.1016/j.crma.2011.03.023}, language = {en}, }
Jean Bourgain; Alex Kontorovich. On Zarembaʼs conjecture. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 493-495. doi : 10.1016/j.crma.2011.03.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.03.023/
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