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math.NT2024

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 and a cuspidal GL eigenform with relatively prime conductors. Then we show that there are infinitely many cusp forms on GL such that…

math.NT2023

Relative Trace Formula, Subconvexity and Quantitative Nonvanishing of Rankin-Selberg -functions for

Liyang Yang

Let be a fixed unitary cuspidal representation of We establish a subconvex bound in the -aspect $$ L(1/2+it,π\timesπ')\ll_{π,π',\varepsilon}(1+…

math.NT2023

Relative Trace Formula and Twisted -functions: the Burgess Bound

Liyang Yang

Let be a number field, either a unitary cuspidal automorphic representation of or a unitary Eisenstein series, and a unitary Hecke character of analy…

math.NT2023

Non-vanishing of twists of -functions

Maksym Radziwiłł, Liyang Yang

Let be a unitary cuspidal automorphic representation of . Let be given. We show that there exists infinitely many primitive e…

math.NT2023

Relative Trace Formula and -functions for

Liyang Yang

We establish a relative trace formula on weighted by cusp forms on over number fields. The spectral side is a weighted average of Rankin-Selberg…