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My research concentrates on analytic number theory and representation theory, in particular, automorphic forms, L-functions and the theory of high-rank Bessel functions.
My research concentrates on analytic number theory and representation theory, in particular, automorphic forms, L-functions and the theory of high-rank Bessel functions.
In Preparation:
In Preparation:
33. joint with Ruihua Qiao, "The Second Moment of GL4×GL2 L-functions at Special Points."
Preprints:
Preprints:
32. "On the Effective Non-vanishing of Hecke–Maass L-functions at Special Points." arXiv:2507.14566 (2025).
31. "On the Effective Non-vanishing of Rankin–Selberg L-functions at Special Points." arXiv:2506.08546 (2025).
29. joint with Changlin Li, "Mean Lindelöf Hypothesis and Prime Geodesic Theorem on Bianchi Manifolds".
28. "On the Symmetric Square Large Sieve for PSL2(Z[i])∖PSL2(C) and the Prime Geodesic Theorem for PSL2(Z[i])∖H3." arXiv:2407.17959 (2024).
27. "On the Twisted Spectral Large Sieve Inequality for PGL2(Z[i])∖PGL2(C)." arxiv:2407.17711 (2024).
26. "On the Spectral Large Sieve Inequality for PGL2(Z[i])∖PGL2(C)." arxiv:2404.09085 (2024).
(The following two preprints have been combined into one (see 5), so they are not for publication.)
"Theory of Bessel Functions of High Rank - II: Hankel Transforms and Fundamental Bessel Kernels." arXiv:1411.6710 (2014).
"Theory of Bessel Functions of High Rank - I: Fundamental Bessel Functions." arXiv:1408.5652 (2014).
Publications：
Publications：
Analytic Number Theory
30. "The Second Moment of GL3×GL2 L-functions at Special Points." Math. Ann., (2025).
24. joint with Zhengxiao Gao and Shu Luo, "Hybrid Weyl-type Bound for p-power Twisted GL(2) L-functions." (in Chinese), Sci. Sin. Math., 54: 593–616, 2024. (arXiv)
23. "Proof of the Strong Ivić Conjecture for the Cubic Moment of Maass-form L-functions." IMRN, no. 22, 19205–19236, 2023. (arXiv)
22. joint with Yongxiao Lin and Ramon M. Nunes. "Strong Subconvexity for Self-dual GL(3) L-functions." IMRN, no.13, 11453–11470, 2023. (arXiv)
21. joint with Sheng-Chi Liu, "Moments of Central L-values for Maass Forms over Imaginary Quadratic Fields." Trans. Amer. Math. Soc., 375, no. 5, 3381–3410, 2022. (arXiv)
19. joint with Roman Holowinsky and Ritabrata Munshi, "Beyond the Weyl Barrier for GL(2) Exponential Sums." Adv. Math. Paper No. 109099, 43 pp, 2023. (arXiv)
18. "Subconvexity for L-Functions on GL3 over Number Fields." J. Eur. Math. Soc. (JEMS), 26, no. 3, 1113–1192, 2024. (arXiv)
17. joint with Qinghua Pi, "Bias of Root Numbers for Modular Newforms of Cubic Level." Proc. Amer. Math. Soc., 149, no. 12, 5035–5047, 2021. (arXiv)
16. joint with Sheng-Chi Liu, "Low-Lying Zeros of L-Functions for Maass Forms over Imaginary Quadratic Fields." Mathematika, 66, no. 3, 777–805, 2020. (arXiv)
15. joint with Keshav Aggarwal, Roman Holowinsky and Yongxiao Lin, "A Bessel Delta Method and Exponential Sums for GL(2)." Q. J. Math., 71, no. 3, 1143–1168, 2020. (arXiv)
12. "Subconvexity for Twisted L-Functions on GL3 over the Gaussian Number Field." Trans. Amer. Math. Soc., 372, no. 12, 8897–8932, 2019. (arXiv)
9. "Cancellation in the Additive Twists of Fourier Coefficients for GL2 and GL3 over Number Fields." Amer. J. Math. 141, no. 5, 1317–1345, 2019. (arXiv)
4. joint with Roman Holowinsky and Ritabrata Munshi, "Character Sums of Composite Moduli and Hybrid Subconvexity." Advances in the Theory of Automorphic Forms and Their L-Functions, 135–148, Contemp. Math., 664, Amer. Math. Soc., Providence, RI, 2016. (arXiv)
3. joint with Roman Holowinsky and Ritabrata Munshi, "Hybrid Subconvexity Bounds for L (1/2, Sym2 f ⊗ g)." Math. Z. 283, no. 1–2, 555–579, 2016. (arXiv)
Representation Theory
20. "A Voronoï–Oppenheim Summation Formula for Number Fields." Acta Arith. 204, no. 3, 269–285, 2022. (arXiv)
13. joint with Chang Yang, "A Whittaker–Plancherel Inversion Formula for SL2(C)." J. Anal. Math., 145, 235–256, 2021. (arXiv)
11. joint with Jingsong Chai, "On the Waldspurger Formula and the Metaplectic Ramanujan Conjecture over Number Fields." J. Funct. Anal. 277, no. 10, 3757–3782, 2019. (arXiv)
10. joint with Jingsong Chai, "Bessel Identities in the Waldspurger Correspondence over the Complex Numbers." Israel J. Math., 235, no. 1, 439–463, 2020. (arXiv)
6. "On the Kuznetsov Trace Formula for PGL2(C)." J. Funct. Anal. 272, no. 8, 3259–3280, 2017. (arXiv)
Analytic Theory of (High-Rank) Bessel Functions
25. "On the Hankel Transform of Bessel Functions on Complex Numbers and Explicit Spectral Formulae over the Gaussian Field." Dedicated to James W. Cogdell for his 70th birthday. J. Funct. Anal. 288, no. 3, 110723, 2025. (arXiv)
14. "On the Fourier Transform of Regularized Bessel Functions on Complex Numbers and Beyond Endoscopy over Number Fields." IMRN, no. 19, 14445–14479, 2021. (arXiv)
8. "On the Fourier Transform of Bessel Functions over Complex Numbers---II: the General Case." Trans. Amer. Math. Soc., 372, no. 4, 2829–2854, 2019. (arXiv)
7. "On the Fourier Transform of Bessel Functions over Complex Numbers---I: the Spherical Case." Monatsh. Math., 186, no. 3, 471–479, 2018. (arXiv)
5. "Theory of Fundamental Bessel Functions of High Rank." Mem. Amer. Math. Soc., 267, no. 1303, vii+123 pp, 2020. (arXiv) (This is a combination of the previous two Bessel papers as well as the first two chapters of my thesis.)
Theory of p-adic Representations
2. "Morita's Duality for Split Reductive Groups." J. Number Theory, 132, 2012.
1. joint with Chang Yang, "Morita's Theory for the Symplectic Groups." Int. J. Number Theory, 07, 2011.
Thesis:
Thesis:
"Theory of Bessel Functions of High Rank." Ph.D. Thesis, the Ohio State University, 2015. (pdf)
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