M. Lang

activity

19942026

most citedFibonacci Numbers and Identities II

7 citations · 15 across the 24 of their papers we have counts for

collaborators

26 papers

math.NT2026

Optimal Farey sequence for the Congruence subgroup $Γ_{0} (2^{n})$

Nhat Minh Doan, Sang-hyun Kim, Mong Lung Lang +1

We prove that $Γ_{0} (2^{n})$ ( $n \geq 2$ ) has a Farey sequence ${e_{i}}$ such that $e_{i} \leq 2^{n - 1}$ for all $e_{i}$ . The above upper bound is optimal, and there exists a unique $j$ such th…

math.NT2022

Optimal independent generating system for the congruence subgroups $Γ_{0} (p)$ and $Γ_{0} (p^{2})$

Nhat Minh Doan, Sang-hyun Kim, Mong Lung Lang +1

Let $n$ be a prime or its square. We prove that the congruence subgroup $Γ_{0} (n)$ admits a free product decomposition into cyclic factors in such a way that the $(2, 1)$ -component of…

math.CO2021

Fibonacci identities and Fibonacci pairs

Cheng Lien Lang, Mong Lung Lang

A Fibonacci pair $F_{s} (w, x)$ of rank $s$ is a pair $s \times s$ nonsingular matrices such that $w x = x w$ and that the entries of $a w^{n}$ and $a x w^{m}$ are polynomials of Fibonacci or Luc…

math.GT2020

Dilogarithm identities after Bridgeman

Pradthana Jaipong, Mong Lung Lang, Ser Peow Tan +1

Following Bridgeman, we demonstrate several families of infinite dilogarithm identities associated with Fibonacci numbers, Lucas numbers, convergents of continued fractions of even…

math.GR2015

Arithmetic and geometry of the Hecke groups

Cheng Lien Lang, Mong Lung Lang

We study the arithmetic and geometry properties of the Hecke group $G_{q}$ . In particular, we prove that $G_{q}$ has a subgroup $X$ of index $d$ , genus $g$ with $v_{\infty}$ cusps, a…

math.NT2015

Identifying normal and congruence subgroups

Cheng Lien Lang, Mong Lung Lang

We give a simple algorithm that enables us to determine whether a subgroup of finite index of the Hecke group is normal.

Optimal Farey sequence for the Congruence subgroup Γ0​(2n)

Optimal independent generating system for the congruence subgroups Γ0​(p) and Γ0​(p2)

Fibonacci identities and Fibonacci pairs

Dilogarithm identities after Bridgeman

Arithmetic and geometry of the Hecke groups

Identifying normal and congruence subgroups

Optimal Farey sequence for the Congruence subgroup $Γ_{0} (2^{n})$

Optimal independent generating system for the congruence subgroups $Γ_{0} (p)$ and $Γ_{0} (p^{2})$