Relative Trace Formula And Simultaneous Nonvanishing for GL_3 x GL_2 and GL_3 x GL_1 L-functions

Philippe Michel, Dinakar Ramakrishnan, Liyang Yang

Fix a Dirichlet character $\chi$ and a cuspidal GL$(2)$ eigenform $\varphi$ with relatively prime conductors. Then we show that there are infinitely many cusp forms $\pi$ on GL$(3)$ such that…