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

Zhi Qi

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

Representation Theory 2018-03-05 v3

Authors: Zhi Qi

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.

Keywords

trace formula gaudin algebras and representation theory

Cite

@article{arxiv.1606.02477,
  title  = {On the Kuznetsov Trace Formula for $\mathrm{PGL}_2(\mathbb{C})$},
  author = {Zhi Qi},
  journal= {arXiv preprint arXiv:1606.02477},
  year   = {2018}
}

Comments

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)

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

Abstract

Keywords

Cite

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