Lulu Fang

activity

20162022

most citedA remark on the extreme value theory for continued fractions

4 citations · 16 across the 13 of their papers we have counts for

collaborators

14 papers

math.NT2022

Dimensions of certain sets of continued fractions with non-decreasing partial quotients

Lulu Fang, Jihua Ma, Kunkun Song +1

Let $[a_{1} (x), a_{2} (x), a_{3} (x), \dots]$ be the continued fraction expansion of $x \in (0, 1)$ . This paper is concerned with certain sets of continued fractions with non-decreasing partia…

math.DS2021

On upper and lower fast Knintchine spectra of continued fractions

Lulu Fang, Lei Shang, Min Wu

Let $ψ : N \to R^{+}$ be a function satisfying $ϕ (n) / n \to \infty$ as $n \to \infty$ . We investigate from a multifractal analysis point of view the growth rate of the s…

math.DS2020★ 1 cited

Precise asymptotics on the Birkhoff sums for dynamical systems

Lulu Fang, Hiroki Takahasi, Yiwei Zhang

We establish two precise asymptotic results on the Birkhoff sums for dynamical systems. These results are parallel to that on the arithmetic sums of independent and identically dis…

math.NT2020

Some exceptional sets of Borel-Bernstein Theorem in continued fractions

Lulu Fang, Jihua Ma, Kunkun Song

Let $[a_{1} (x), a_{2} (x), a_{3} (x), \dots]$ denote the continued fraction expansion of a real number $x \in [0, 1)$ . This paper is concerned with certain exceptional sets of the Borel-Bern…

math.NT2019★ 3 cited

Multifractal analysis of the convergence exponent in continued fractions

Fang Lulu, Song Kunkun

Let $x \in [0, 1)$ be a real number and denote its continued fraction expansion by $[a_{1} (x), a_{2} (x), a_{3} (x), \dots]$ . The convergence exponent of these partial quotients is defined a…

math.DS2018★ 2 cited

A note on the run length function for intermittency maps

Hongfei Cui, Lulu Fang, Yiwei Zhang

We study the run length function for intermittency maps. In particular, we show that the longest consecutive zero digits (resp. one digits) having a time window of polynomial (resp…

math.NT2016★ 4 cited

A remark on the extreme value theory for continued fractions

Lulu Fang, Kunkun Song

Let $x$ be a irrational number in the unit interval and denote by its continued fraction expansion $[a_{1} (x), a_{2} (x), \dots, a_{n} (x), \dots]$ . For any $n \geq 1$ , write $T_n(x) = \…

math.NT2016★ 1 cited

The denominators of convergents for continued fractions

Lulu Fang, Min Wu, Bing Li

For any real number $x \in [0, 1)$ , we denote by $q_{n} (x)$ the denominator of the $n$ -th convergent of the continued fraction expansion of $x$ $(n \in N)$ . It is well-known…

math.ST2016★ 3 cited

A note on Rényi's "record" problem and Engel's series

Lulu Fang, Min Wu

In 1973, Williams introduced two interesting discrete Markov processes, namely $C$ -processes and $A$ -processes, which are related to record times in statistics and Engel's series i…

math.PR2016★ 1 cited

Large and moderate deviation principles for Engel continued fractions

Lulu Fang, Lei Shang

Large and moderate deviation principles are proved for Engel continued fractions, a new type of continued fraction expansion with non-decreasing partial quotients in number theory.

math.NT2016★ 1 cited

Beta-expansion and continued fraction expansion of real numbers

Lulu Fang, Min Wu, Bing Li

Let $β > 1$ be a real number and $x \in [0, 1)$ be an irrational number. We denote by $k_{n} (x)$ the exact number of partial quotients in the continued fraction expansion of $x$ given…

math.NT2016

Approximation orders of real numbers by $β$ -expansions

Lulu Fang, Min Wu, Bing Li

We prove that almost all real numbers (with respect to Lebesgue measure) are approximated by the convergents of their $β$ -expansions with the exponential order $β^{- n}$ . Moreover,…

math.NT2016

Random Continued fractions: Lévy constant and Chernoff-type estimate

Lulu Fang, Min Wu, Narn-Rueih Shieh +1

Given a stochastic process ${A_{n}, n \geq 1}$ taking values in natural numbers, the random continued fractions is defined as $[A_{1}, A_{2}, \dots, A_{n}, \dots]$ analogue to the cont…

math.NT2016

Limit theorems related to beta-expansion and continued fraction expansion

Lulu Fang, Min Wu, Bing Li

Let $β > 1$ be a real number and $x \in [0, 1)$ be an irrational number. Denote by $k_{n} (x)$ the exact number of partial quotients in the continued fraction expansion of $x$ given by…

Dimensions of certain sets of continued fractions with non-decreasing partial quotients

On upper and lower fast Knintchine spectra of continued fractions

Precise asymptotics on the Birkhoff sums for dynamical systems

Some exceptional sets of Borel-Bernstein Theorem in continued fractions

Multifractal analysis of the convergence exponent in continued fractions

A note on the run length function for intermittency maps

A remark on the extreme value theory for continued fractions

The denominators of convergents for continued fractions

A note on Rényi's "record" problem and Engel's series

Large and moderate deviation principles for Engel continued fractions

Beta-expansion and continued fraction expansion of real numbers

Approximation orders of real numbers by β-expansions

Random Continued fractions: Lévy constant and Chernoff-type estimate

Limit theorems related to beta-expansion and continued fraction expansion

Approximation orders of real numbers by $β$ -expansions