Семинар Добрушинской математической лаборатории ИППИ РАН
15 сентября, вторник, 16:00 пройдет в режиме онлайн-конференции
на платформе Zoom.
Илья Шкредов (ИППИ): Zaremba"s conjecture and growth in groups
Абстракт:
Zaremba"s conjecture belongs to the area of continued fractions.
It predicts that for any given positive integer q there is a positive
a, a<q, (a,q)=1 such that all partial quotients b_j in its continued
fractions expansion a/q = 1/b_1+1/b_2 +... + 1/b_s are bounded
by five. At the moment the question is widely open although the
area has a rich history of works by Korobov, Hensley, Niederreiter,
Bourgain and many others. We survey certain results concerning
this hypothesis and show how growth in groups helps to solve
different relaxations of Zaremba"s conjecture. In particular, we
show that a deeper hypothesis of Hensley concerning some
Cantor-type set with the Hausdorff dimension >1/2 takes place f
or the so-called modular form of Zaremba"s conjecture.
Ссылка для подключения:
https://zoom.us/j/93175142429?pwd=VDViRHNOSlZSVUM5ZU03SGZyZy8xQT09
Id: 931-7514-2429 passw=057376
| 10.09.2020 | Комеч Сергей Александрович |