A strengthening of a theorem of Bourgain and Kontorovich. V
- Авторлар: Kan I.D.1
-
Мекемелер:
- Moscow Aviation Institute (National Research University)
- Шығарылым: Том 296, № 1 (2017)
- Беттер: 125-131
- Бөлім: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/174217
- DOI: https://doi.org/10.1134/S0081543817010102
- ID: 174217
Дәйексөз келтіру
Аннотация
It is proved that the denominators of finite continued fractions all of whose partial quotients belong to an arbitrary finite alphabet A with parameter δ > 0.7807... (i.e., such that the set of infinite continued fractions with partial quotients from this alphabet is of Hausdorff dimension δ with δ > 0.7807... ) contain a positive proportion of positive integers. Earlier, a similar theorem has been obtained only for alphabets with somewhat greater values of δ. Namely, the first result of this kind for an arbitrary finite alphabet with δ > 0.9839... is due to Bourgain and Kontorovich (2011). Then, in 2013, D.A. Frolenkov and the present author proved such a theorem for an arbitrary finite alphabet with δ > 0.8333.... The preceding result of 2015 of the present author concerned an arbitrary finite alphabet with δ > 0.7862....
Авторлар туралы
I. Kan
Moscow Aviation Institute (National Research University)
Хат алмасуға жауапты Автор.
Email: igor.kan@list.ru
Ресей, Volokolamskoe sh. 4, Moscow, 125993
Қосымша файлдар
