M. Lang

activity

19942026

most citedFibonacci Numbers and Identities II

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

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14 papers · 1 filter

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.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.

math.NT2014

Wohlfahrt's Theorem and index formula for elementary matrix groups and $S L (2, O)$

Cheng Lien Lang, Mong Lung Lang

The present article determines the indices of the principal congruence subgroups of the Bianchi groups $B_{d}$ , $S L (2, O)$ and elementary matrix group $E$ and extends Wohlfah…

math.NT2013

Three term recurrence and residue completeness

Cheng Lien Lang, Mong Lung Lang

We study the three term recurrence modulo m. In particular, we prove that Pell numbers modulo m is residue complete if and only m is 2, a power of 3, or a power of 5. Pell-Lucas nu…

math.NT2013

Generalised Binomial coefficients and Jarden's Theorem

Cheng Lien Lang, Mong Lung Lang

We prove a stronger version of Jarden's Theorem for recurrence of powers of recursive functions

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

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

Identifying normal and congruence subgroups

Wohlfahrt's Theorem and index formula for elementary matrix groups and SL(2,O)

Three term recurrence and residue completeness

Generalised Binomial coefficients and Jarden's Theorem

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

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

Wohlfahrt's Theorem and index formula for elementary matrix groups and $S L (2, O)$