On the Kuznetsov Trace Formula for PGL₂(ℂ)

2016/06/08 by Zhi Qi, Qi, Zhi
Mathematics · #Advanced Algebra and Geometry #Mathematical Analysis and Transform Methods #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.1606.02477

Abstract

In this note, using a representation theoretic method of Cogdell and Piatetski-Shapiro, we prove the Kuznetsov trace formula for an arbitrary discrete group Γ in PGL₂(ℂ) that is cofinite but not cocompact. An essential ingredient is a kernel formula, recently proved by the author, on Bessel functions for PGL₂(ℂ). This approach avoids the difficult analysis in the existing method due to Bruggeman and Motohashi.

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