Relative Trace Formula and L-functions for GL(n+1)× GL(n)

2023/03/03 by Liyang Yang, Yang, Liyang
Mathematics · Arts and Humanities · #Advanced Algebra and Geometry #Analytic Number Theory Research #Historical Studies and Socio-cultural Analysis

paper · pdf · doi:10.48550/arxiv.2303.02225

Abstract

We establish a relative trace formula on GL(n+1) weighted by cusp forms on GL(n) over number fields. The spectral side is a weighted average of Rankin-Selberg L-functions for GL(n+1)\timesGL(n) over the full spectrum, and the geometric side consists of Rankin-Selberg L-functions for GL(n)\timesGL(n), and certain explicit holomorphic functions. The formula yields new results towards central L-values for GL(n+1)\timesGL(n) (over number fields): the second moment evaluation, and simultaneous nonvnaishing in the level aspect.

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