The weight two and opposite sign cases for the Fourier relative trace formulas
Abstract
We provide an adelic relative trace formula proof to the Petersson/Bruggeman-Kuznetsov (PBK) formulas, specifically in the holomorphic case for =2 and the non-holomorphic case for m1m2<0. Given two sets of hypothesis on the non archimedean test function f, called the geometric and spectral assumptions, this approach allows us to obtain refined PBK formulas.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.