Zheng Liu

I am an assistant professor at the University of California, Santa Barbara. I received my Ph.D. from Columbia University in 2016 under the supervision of  Eric Urban. My research area is number theory, in particular p-adic properties of automorphic forms and special L-values and Iwasawa theory.

Research:

• $p$-adic $L$-functions for GSp(4)$\times$GL(2) II, submitted
• $p$-adic $L$-functions for GSp(4)$\times$GL(2), submitted
• Derived p-adic heights and the leading coefficient of the Bertolini-Darmon-Prasanna p-adic L-function, (with Francesc Castella, Chi-Yun Hsu, Debanjana Kundu, Yu-Sheng Lee), submitted
  
• Iwasawa Greenberg main conjecture for non-ordinary modular forms and Eisenstein congruences on GU(3,1) (with Francesc Castella and Xin Wan), submitted
  
• Archimedean zeta integrals for unitary groups (with Ellen Eischen), to appear in J. Reine Angew. Math.
• Ordinary families of Klingen Eisenstein series on symplectic groups, Trans. Amer. Math. Soc. 374(5):3331-3395, 2021
• The doubling Archimedean zeta integrals for p-adic interpolation, Math. Res. Lett. 28(1):145-173, 2021
• Differential operators and the doubling archimedean zeta integrals, RIMS Kokyuroku 2197:22-37, 2021
• Non-cuspidal Hida theory for Siegel modular forms and trivial zeros of p-adic L-functions (with Giovanni Rosso), Math. Ann. 378 (2020), no.1, 153-231
  
• $p$-adic $L$-functions for ordinary families on symplectic groups, J. Inst. Math. Jussieu.19(4):1287-1347, 2020
  
• Nearly overconvergent Siegel modular forms, Ann. Inst. Fourier (Grenoble), 69 (2019), no. 6, 2439--2506