On the Kuznetsov trace formula for PGL2(C)

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.