Hang Xue

Interests

Research

Number Theory, Automorphic forms, Arithmetic Geometry

Courses

Scholarly Contributions

Books

• Xue, H. (2024). Automorphic forms beyond GL2. AMS Sureys and Monographs in Mathematics.

Journals/Publications

• Xue, H., & Suzuki, M. (2023). Linear intertwining periods and epsilon dichotomy for linear models. Math Ann. doi:https://doi.org/10.1007/s00208-023-02615-9
• Xue, H. (2023). Bessel models for real unitary groups: the tempered case. Duke Math Journal, 172(5), 995-1031. doi:DOI: 10.1215/00127094-2022-0018
• Xue, H. (2022). Orbital integral on GL_n \times GL_n \ GL_2n. Canadian Math Journal. doi:doi:10.4153/S0008414X21000122
• Xue, H. (2021). Epsilon dichotomy for linear models. Algebra & Number Theory. doi:10.2140/ant.2021.15.173
• Xue, H. (2021). Epsilon dichotomy for linear models. Algebra Number Theory. doi:DOI: 10.2140/ant.2021.15.173
• Xue, H. (2021). Orbital integrals on. Canadian Journal of Mathematics. doi:10.4153/s0008414x21000122
• Xue, H. (2019). Arithmetic theta lifts and arithmetic Gan--Gross--Prasad conjecture for unitary groups. Duke Math Journal.
• Xue, H. (2019). On the global Gan–Gross–Prasad conjecture for unitary groups: Approximating smooth transfer of Jacquet–Rallis. Crelle's Journal, 2019(756), 65-100. doi:10.1515/crelle-2017-0016
  More info

  Abstract Zhang proved the global Gan–Gross–Prasad conjecture for \operatorname{U}(n+1)\times\operatorname{U}(n) under some local conditions [19]. One of the conditions is that the unitary groups are split at the archimedean places. We remove this assumption at the archimedean places in this paper.
• Xue, H. (2019). On the global Gan--Gross--Prasad conjecture for unitary groups: approximating smooth transfer of Jacquet--Rallis. Crelle's Journal.
• Xue, H. (2017). Refined global Gan–Gross–Prasad conjecture for Fourier–Jacobi periods on symplectic groups. Compositio Mathematica. doi:10.1112/s0010437x16007752
• Xue, H. (2017). Refined global Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on symplectic groups. Compositio Mathematica.
• Xue, H. (2018). Fourier–Jacobi periods of classical Saito–Kurokawa lifts. Ramanujan Journal.
• Xue, H. (2016). Fourier–Jacobi periods and the central value of Rankin–Selberg L-functions. Israel Journal of Mathematics. doi:10.1007/s11856-016-1300-2
• Xue, H. (2015). A quadratic point on the Jacobian of the universal genus four curve. Mathematical Research Letters. doi:10.4310/mrl.2015.v22.n5.a13
• Xue, H. (2014). The Gan–Gross–Prasad conjecture forU(n)×U(n). Advances in Mathematics. doi:10.1016/j.aim.2014.06.010
  More info

  We prove the Gan–Gross–Prasad conjecture for U ( n ) × U ( n ) under some local conditions using a relative trace formula. We deduce some new cases of the Gan–Gross–Prasad conjecture for U ( n + 1 ) × U ( n ) from the case of U ( n ) × U ( n ) .