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

• Boisseau, P., Lu, W., & Xue, H. (2026). The global Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups I: Coarse expansions of the relative trace formulae.
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  This is the first of a series of three papers where we prove the Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups and an Ichino--Ikeda type refinement. Our strategy is based on the comparison of relative trace formulae formulated by Liu. The goal of this first paper is to introduce the relative trace formulae and establish the coarse expansions.[Journal_ref: ]
• Boisseau, P., Lu, W., & Xue, H. (2026). The global Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups II: Comparison of the relative trace formulae.
  More info

  This is the second of a series of three papers where we prove the Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups and an Ichino--Ikeda type refinement. Our strategy is based on the comparison of relative trace formulae formulated by Liu. The goal of this second paper is to compare the two relative trace formulae.[Journal_ref: ]
• Boisseau, P., Lu, W., & Xue, H. (2026). The global Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups III: Proof of the main theorems.
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  This is the third and the last of a series of three papers where we prove the Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups and an Ichino--Ikeda type refinement. Our strategy is based on the comparison of relative trace formulae formulated by Liu. In this paper, we compute the spectral expansions of these formulae and end the proof of the conjectures via a reduction to the corank zero case.[Journal_ref: ]
• Geng, Z., & Xue, H. (2026). Casselman-Wallach property for homological theta lifting.
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  In this paper, we establish the Casselman-Wallach property for homological theta lifting over archimedean local fields. As a consequence, the Euler-Poincaré characteristic is a well-defined element in the Grothendieck group of Casselman-Wallach representations. Our main tool is a corank-one parabolic stable filtration on the Weil representation.[Journal_ref: ]
• 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
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  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
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  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 ) .