Liyang Yang

I am a fifth-year graduate student at California Institute of Technology. My advisor is Dinakar Ramakrishnan .

Previously I graduated from Tsinghua University in June 2016. Here is my CV.

- Number Theory, Automorphic Representation and Arithmetic Geometry

Average of Dirichlet Coefficients of Cuspidal Representations Related to GL(2). The Ramanujan Journal, (2020). To appear.

(with Dinakar Ramakrishnan) A Constraint for Twist Equivalence of Cusp Forms on GL(n). Functiones et Approximatio Commentarii Mathematici, (2020). To appear.

An Explicit CM Type Norm Formula and Effective Nonvanishing of Class Group L-functions for CM Fields. Pacific Journal of Mathematics 304.1 (2020): 347-384.

Diophantine Inequalities Involving a Prime and an Almost-prime. Journal of Number Theory, 170 (2017), 347-367.

(with Daniel Goldston) The Average Number of Goldbach Representations, in Prime Numbers and Representation Theory, Lecture Series of Modern Number Theory, volume 2, (2017), 1-12.

(with Philippe Michel and Dinakar Ramakrishnan) Average Central L-values on U(3)\times U(2), Nonvanishing and Subconvexity. Preprint.

(with Maksym Radziwill) Nonvanihsing of Twists of GL(4) L-functions. Preprint.

(with Liubomir Chiriac) Summing Hecke Eigenvalues over Polynomials, submitted.

Arithmetic Distribution of Tempered Components of Cuspidal Representations on GL(3). Preprint.

Holomorphy of Adjoint L-functions for GL(n): n\leq 4, submitted.

A Coarse Jacquet-Zagier Trace Formula for GL(n) with Applications, submitted.

An Introduction to Trace Formula Approach. In process, available upon request.

- An Outline of the Proof to Entireness of Adjoint L-functions.
- Archimedean Zeta Integrals of Quaternion Algebras.
- On the Subconvexity Problem and Equidistribution of Heegner Points.