On the rate of convergence of continued fraction statistics of random rationals
김수현
온라인
0
1668
2025.09.15 09:25
| 구분 | 기타 |
|---|---|
| 일정 | 2025-09-17(수) 09:30~10:30 |
| 세미나실 | 온라인 |
| 강연자 | 김태형 (Brandeis University) |
| 담당교수 | 임선희 |
| 기타 | 동역학-정수론 |
줌 회의 ID: 980 403 2023 암호: dynamics
초록: The statistical behavior of continued fraction expansions for typical real numbers is a classic subject, such as the Lévy-Khintchine Theorem. A natural question arises when we restrict our attention to the set of rational numbers. In 2018, David and Shapira showed that the continued fraction statistics of random rationals with a fixed denominator converge to the Gauss–Kuzmin distribution as the denominator grows. In this talk, we will present our recent result establishing a polynomial rate of convergence for these statistics. Our approach relies on an equidistribution result for divergent orbits of the geodesic flow on SL(2,R)/SL(2,Z), combined with entropy bounds for invariant measures that spend significant time in the cusp.
This is joint work with Ofir David, Ron Mor, and Uri Shapira.
