2021/10/22 by Xinchen Miao, Miao, Xinchen
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.2110.11529
31 pages. This is a preliminary draft. All comments are welcome!
arxiv created 2021/10/22 · openalex publication_date 2021/10/22 · arxiv updated 2021/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a new case of spectral reciprocity formulae for the product of GL(n+1) × GL(n) and GL(n) × GL(n-1) Rankin-Selberg L-functions (n ≥ 3), which are first developed by Blomer and Khan in \citeBK17 for degree 8 L-functions (n=2 case, the product of GL(3) × GL(2) and GL(2) × GL(1) Rankin-Selberg L-functions). Our result can be viewed as a generalization of Blomer and Khan's work to higher rank case. We will mainly follow the method developed in \citeNun20. We will use the integral representations of Rankin-Selberg L-functions generalized by Ichino and Yamana \citeIY15, spectral theory of L2 space and the language of automorphic representations.