Deducing Selberg trace formula via Rankin-Selberg method for $\mathrm{GL}_2$
Number Theory
2022-06-22 v3
Abstract
In the 80s, Zagier and Jacquet-Zagier tried to derive the Selberg trace formula by applying the Rankin-Selberg method to the automorphic kernel function. Their derivation was incomplete due to a puzzle of the computation of a residue. We solve this puzzle and complete the derivation. The main input is an extension of the theory of regularized integrals invented by Zagier, which is of independent interest.
Keywords
Cite
@article{arxiv.1810.09437,
title = {Deducing Selberg trace formula via Rankin-Selberg method for $\mathrm{GL}_2$},
author = {Han Wu},
journal= {arXiv preprint arXiv:1810.09437},
year = {2022}
}
Comments
final version, accepted by Transactions of the AMS. arXiv admin note: substantial text overlap with arXiv:1610.00230