9 papers · 1 filter
Ideal class monoids of cubic orders
Sungmun Cho, Jungtaek Hong, Yuchan Lee
Let be an order in a number field, let be its ideal class monoid, and let act on it by multiplication. The local-global product for…
Beyond Endoscopy for : Functional equation for the -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…
An upper bound for the size of the ideal class monoid
Sungmun Cho, Jungtaek Hong, Yuchan Lee
The ideal class monoid for an order in a finite field extension of a number field, denoted by , is a fundamental object to study in number theo…
Diophantine analysis and Arthur's trace formula
Yuchan Lee
Let be a -homogeneous space over a number field such that . Here, is a simply connected semisimple group over and whose centr…
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 of degree , where is a number field and its ring of integers, let denote the number of $n…
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…