3 papers
math.NT2026
Congruence Classes of Supporting the Erdös-Straus Conjecture I: Tame Solutions
Xiaoping Xu
In 1948, Erdös and Straus formulated a conjecture : for any positive integer , there exist positive integers and such that \begin{equation}\frac{4}{n}=\frac{1…
math.RT2025
Hilbert Polynomials of Noncanonical Orthogonal Oscillator Representations of
Hengjia Zhang, Xiaoping Xu
By applying Fourier transformations to the natural orthogonal oscillator representations of special linear Lie algebras, Luo and the second author (2013) obtained a large family of…
math.RT2025
Orthogonal Oscillator Representations, Laplace Equations and Intersections of Determinantal Varieties
Hengjia Zhang, Xiaoping Xu
Associated varieties are geometric objects appearing in infinite-dimensional representations of semisimple Lie algebras (groups). By applying Fourier transformations to the natural…