6 papers
On the restriction norm of large level
Chengliang Guo
In this paper, we prove the mass equidistribution theorem restricted to vertical geodesic segments for holomorphic Hecke newforms of large square-free level. We utilize the effecti…
On the -norm of holomorphic Hecke eigenforms
Chengliang Guo, Liangxun Li
Let be an -normalized Hecke basis for the space of all holomorphic cusp forms of weight . We show that w…
Mixed fourth moments of automorphic forms and the shifted moments of -functions
Chengliang Guo
In this article, we study the mixed fourth moments of Hecke--Maass cusp forms and Eisenstein series with type . Under the assumptions of the Generalized Riemann Hypothesis…
Joint cubic moment of Eisenstein series and Hecke-Maass cusp forms
Chengliang Guo
Let be a smooth compactly supported function on . In this paper, we are interested in the joint cubic moments of automorphic…
A New proof of Liouville type theorems for a class of semilinear elliptic equations
Chen Guo, Zhengce Zhang
We study certain typical semilinear elliptic equations in Euclidean space $\bR^{n}$ or on a closed manifold with nonnegative Ricci curvature. Our proof is based on a crucial in…
Gradient Estimates for the doubly nonlinear diffusion equation on Complete Riemannian Manifolds
Chen Guo, Zhengce Zhang
We study the elliptic version of doubly nonlinear diffusion equations on a complete Riemannian manifold . Through the combination of a special nonlinear transformation and t…