2024/11/19 by Philippe Michel, Dinakar Ramakrishnan, Michel, Philippe +3
Computer Science · Mathematics · #11F66 (secondary) #11F70 #11G99 (primary) #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2411.12609
openalex publication_date 2024/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fix a Dirichlet character χ and a cuspidal GL(2) eigenform ϕ with relatively prime conductors. Then we show that there are infinitely many cusp forms π on GL(3) such that L(1/2, π× χ) and L(1/2, π× ϕ) are simultaneously non-zero. We achieve this by use of Jacquet's Relative Trace Formula. We derive an expression of the average over the GL(3) cuspidal spectrum as a sum of a non-zero main term and two subsidiary terms which are forced to be zero for large enough level by use of a suitable test function. This modest article is dedicated to the memory of Harish Chandra, on the occasion of his hundredth birthday.