Seungjai Lee

activity

20162026

collaborators

9 papers

math.RA2026

Zeta functions of solvable Lie algebras over finite fields -- with calculations in detail

Seungjai Lee

Let $L$ be a solvable Lie algebra of dimension less than or equal to 4 over finite fields. We compute and record, in explicit symbolic form, the zeta functions enumerating subalgeb…

math.RA2022

Uniformity in Higher class Free Lie algebras

Marcus du Sautoy, Seungjai Lee

Let $f_{c, 2}$ denote a free class- $c$ Lie rings on $2$ generators. We investigate the zeta functions enumerating graded ideals in $f_{c, 2} (F_{p})$ for…

math.GR2021

The groups and nilpotent Lie rings of order $p^{8}$ with maximal class

Seungjai Lee, Michael Vaughan-Lee

We classify the nilpotent Lie rings of order $p^{8}$ with maximal class for $p \geq 5$ . This also provides a classification of the groups of order $p^{8}$ with maximal class for $p \ge…

math.CO2020

Hilbert quasipolynomials and their roots

Seungjai Lee

We investigate the roots of Hilbert quasipolynomials arising from certain rational generating functions.

math.GR2020

Normal zeta functions of small $T_{2}$ -groups and their behaviour on residue classes

Seungjai Lee

Let $G$ be a finitely generate nilpotent class-2 torsion-free group. We study how the zeta function enumerating normal subgroups of G varies on residue classes. In particular, we s…

math.RA2020

Zeta functions of $F_{p}$ -Lie algebras and finite $p$ -groups

Seungjai Lee

We study zeta functions enumerating subalgebras or ideals of Lie algebras over finite field of prime order $F_{p}$ . We first develop a general blueprint method for computing…

math.RA2020

Zeta functions of integral nilpotent quiver representations

Seungjai Lee, Christopher Voll

We introduce and study multivariate zeta functions enumerating subrepresentations of integral quiver representations. For nilpotent such representations defined over number fields,…

math.RA2016

Enumerating graded ideals in graded rings associated to free nilpotent Lie rings

Seungjai Lee, Christopher Voll

We compute the zeta functions enumerating graded ideals in the graded Lie rings associated with the free $d$ -generator Lie rings $f_{c, d}$ of nilpotency class $c$ for al…

math.NT2016

On the twisted quadratic moment for Dirichlet L-functions

Seok Hyeong Lee, Seungjai Lee

Given $c,$ a positive integer, we give an explicit formula and an asymptotic formula for \[ \sumχ(c)|L(1,\,χ)|^{2}, \] where $χ$ is the non-trivial Dirichlet character mod $f$ with…

Zeta functions of solvable Lie algebras over finite fields -- with calculations in detail

Uniformity in Higher class Free Lie algebras

The groups and nilpotent Lie rings of order p8 with maximal class

Hilbert quasipolynomials and their roots

Normal zeta functions of small T2​-groups and their behaviour on residue classes

Zeta functions of Fp​-Lie algebras and finite p-groups

Zeta functions of integral nilpotent quiver representations

Enumerating graded ideals in graded rings associated to free nilpotent Lie rings

On the twisted quadratic moment for Dirichlet L-functions

The groups and nilpotent Lie rings of order $p^{8}$ with maximal class

Normal zeta functions of small $T_{2}$ -groups and their behaviour on residue classes

Zeta functions of $F_{p}$ -Lie algebras and finite $p$ -groups