Deducing Selberg trace formula via Rankin-Selberg method for ${\mathrm{GL}}_2$

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.

final version, accepted by Transactions of the AMS. arXiv admin note: substantial text overlap with arXiv:1610.00230

References in corpus (1)

• A Note on Spectral Analysis for ${\mathrm{GL}}_2$: I

Cited by in corpus (5)

• On Kuznetsov-Bykovskii's formula of counting prime geodesics
• Quantum Unique Ergodicity for Eisenstein Series in the Level Aspect
• Explicit subconvexity for ${\mathrm{GL}}_2$
• A Coarse Jacquet-Zagier Trace Formula for GL($n$) with Applications
• On Weyl's Subconvex Bound for Cube-Free Hecke characters: Totally Real Case