Yuchan Lee

activity

20232026

collaborators

9 papers

math.NT2026

Ideal class monoids of cubic orders

Sungmun Cho, Jungtaek Hong, Yuchan Lee

Let $R$ be an order in a number field, let $Cl (R)$ be its ideal class monoid, and let $Cl (R)$ act on it by multiplication. The local-global product for…

math.NT2026

Beyond Endoscopy for $GL_{3} (Q)$ : Functional equation for the $L$ -function of a cubic order

Yuchan Lee

The Beyond Endoscopy strategy, proposed by Langlands, aims to establish the principle of functoriality by analyzing the trace formula. Recently, Deng and Espinosa advanced this pro…

math.NT2025

An upper bound for the size of the ideal class monoid

Sungmun Cho, Jungtaek Hong, Yuchan Lee

The ideal class monoid for an order $R$ in a finite field extension $E / F$ of a number field, denoted by $Cl (R)$ , is a fundamental object to study in number theo…

math.NT2025

Diophantine analysis and Arthur's trace formula

Yuchan Lee

Let $X$ be a $G$ -homogeneous space over a number field $k$ such that $X ≅ G_{γ} \ G$ . Here, $G$ is a simply connected semisimple group over $k$ and $γ \in G (k)$ whose centr…

math.NT2025

An asymptotic formula for the number of integral matrices with a fixed characteristic polynomial via orbital integrals

Seongsu Jeon, Yuchan Lee

For an irreducible polynomial $χ (x) \in O_{k} [x]$ of degree $n$ , where $k$ is a number field and $O_{k}$ its ring of integers, let $N (X, T)$ denote the number of $n…

math.NT2024

Stable orbital integrals for classical Lie algebras and smooth integral models

Sungmun Cho, Taeyeoup Kang, Yuchan Lee

A main goal of this paper is to introduce a new description of the stable orbital integral for a regular semisimple element and for the unit element of the Hecke algebra in the cas…

math.NT2024

Orbital integrals and ideal class monoids for a Bass order

Sungmun Cho, Jungtaek Hong, Yuchan Lee

A Bass order is an order in a number field for which every fractional ideal can be generated by two elements. Examples include quadratic orders, orders containing the maximal order…

math.NT2024

An explicit formula for the orbital integrals on the spherical Hecke algebra of $GL_{3}$

Sungmun Cho, Yuchan Lee

We provide the explicit formula for orbital integrals associated with elliptic regular semisimple elements in $GL_{n} (F) \cap M_{n} (o)$ and associated with…

math.NT2023

On a Kostant section for the unitary group

Yuchan Lee

For the unitary group defined over the ring of integers in a non Archimedean local field, we give a correction for a Kostant section provided in G.Laumon and B.C. Ngô's paper; Le l…

Ideal class monoids of cubic orders

Beyond Endoscopy for GL3​(Q): Functional equation for the L-function of a cubic order

An upper bound for the size of the ideal class monoid

Diophantine analysis and Arthur's trace formula

An asymptotic formula for the number of integral matrices with a fixed characteristic polynomial via orbital integrals

Stable orbital integrals for classical Lie algebras and smooth integral models

Orbital integrals and ideal class monoids for a Bass order

An explicit formula for the orbital integrals on the spherical Hecke algebra of GL3​

On a Kostant section for the unitary group

Beyond Endoscopy for $GL_{3} (Q)$ : Functional equation for the $L$ -function of a cubic order

An explicit formula for the orbital integrals on the spherical Hecke algebra of $GL_{3}$