On the Kuznetsov Trace Formula for ${\mathrm{PGL}}_2(\mathbb{C})$

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 $\Gamma$ in ${\mathrm{PGL}}_2(\mathbb{C})$ that is cofinite but not cocompact. An essential ingredient is a kernel formula, recently proved by the author, on Bessel functions for ${\mathrm{PGL}}_2(\mathbb{C})$. This approach avoids the difficult analysis in the existing method due to Bruggeman and Motohashi.

19 pages. J. Funct. Anal. Some calculations and statements for complementary series are simplified (corrected), in which case d should be 0 (not an arbitrary integer)

References in corpus (1)

• Theory of Fundamental Bessel Functions of High Rank