Zheng Liu

activity

20182026

most citedNon-cuspidal Hida theory for Siegel modular forms and trivial zeros of

p

-adic

L

-functions

6 citations · 12 across the 7 of their papers we have counts for

collaborators

7 papers

math.NT2026

Kato's main conjecture for nonordinary modular forms

Francesc Castella, Zheng Liu, Xin Wan

We prove Kato's main conjecture for modular forms at nonordinary primes for weights in the Fontaine-Laffaille range. The key ingredients in the proof are a reformulation of the con…

math.NT2023

$p$ -adic $L$ -functions for $GSp (4) \times GL (2)$

Zheng Liu

We construct $p$ -adic $L$ -functions interpolating the critical values of the degree eight $L$ -functions of $GSp (4) \times GL (2)$ for cuspidal automorphic representations…

math.NT2023

Derived $p$ -adic heights and the leading coefficient of the Bertolini--Darmon--Prasanna $p$ -adic $L$ -function

Francesc Castella, Chi-Yun Hsu, Debanjana Kundu +2

Let $E / Q$ be an elliptic curve and let $p$ be an odd prime of good reduction for $E$ . Let $K$ be an imaginary quadratic field satisfying the classical Heegner hypothesis a…

math.NT2021★ 1 cited

Iwasawa-Greenberg main conjecture for non-ordinary modular forms and Eisenstein congruences on $GU (3, 1)$

Francesc Castella, Zheng Liu, Xin Wan

In this paper we prove one side divisibility of the Iwasawa-Greenberg main conjecture for Rankin-Selberg product of a weight two cusp form and an ordinary CM form of higher weight,…

math.NT2020★ 2 cited

Archimedean Zeta Integrals for Unitary Groups

Ellen Eischen, Zheng Liu

We derive precise formulas for the archimedean Euler factors occurring in certain standard Langlands $L$ -functions for unitary groups. In the 1980s, Paul Garrett, as well as Ilya P…

math.NT2019★ 3 cited

The doubling Archimedean zeta integrals for p-adic interpolation

Zheng Liu

We compute the Archimedean doubling zeta integrals which appear in the interpolation formulas for the p-adic L-functions of Siegel modular forms, and verify that they agree with th…

math.NT2018★ 6 cited

Non-cuspidal Hida theory for Siegel modular forms and trivial zeros of $p$ -adic $L$ -functions

Zheng Liu, Giovanni Rosso

We study the derivative of the standard $p$ -adic $L$ -function associated with a $P$ -ordinary Siegel modular form (for $P$ a parabolic subgroup of $GL (n)$ ) when it presents…

Kato's main conjecture for nonordinary modular forms

p-adic L-functions for GSp(4)×GL(2)

Derived p-adic heights and the leading coefficient of the Bertolini--Darmon--Prasanna p-adic L-function

Iwasawa-Greenberg main conjecture for non-ordinary modular forms and Eisenstein congruences on GU(3,1)

Archimedean Zeta Integrals for Unitary Groups

The doubling Archimedean zeta integrals for p-adic interpolation

Non-cuspidal Hida theory for Siegel modular forms and trivial zeros of p-adic L-functions

$p$ -adic $L$ -functions for $GSp (4) \times GL (2)$

Derived $p$ -adic heights and the leading coefficient of the Bertolini--Darmon--Prasanna $p$ -adic $L$ -function

Iwasawa-Greenberg main conjecture for non-ordinary modular forms and Eisenstein congruences on $GU (3, 1)$

Non-cuspidal Hida theory for Siegel modular forms and trivial zeros of $p$ -adic $L$ -functions